Sequences and Nth Term

GCSE Maths Algebra Sequences and Nth Term

Sequences

A sequence is an ordered list of numbers, called terms, that follow a specific pattern or rule. Each number in the sequence is referred to as a term, and the position of a term in the sequence is its term number.

There are many types of sequences, but the most common ones are:

Arithmetic sequences – The difference between consecutive terms is constant. For example, the sequence 1, 3, 5, 7, 9… is an arithmetic sequence with a common difference of 2.

Geometric sequences – The ratio between consecutive terms is constant. For example, the sequence 2, 4, 8, 16, 32… is a geometric sequence with a common ratio of 2.

Quadratic sequences – The difference between consecutive terms grows linearly. In other words, the difference between consecutive terms is itself an arithmetic sequence. For example, the sequence 1, 4, 9, 16, 25… is a quadratic sequence, since the difference between consecutive terms is the arithmetic sequence 3, 5, 7, 9, …

Generating sequences

Generating terms of a sequence can be done using either a term-to-term rule or a position-to-term rule.

Term-to-term rule: Each term is generated based on the previous term(s) following a specific pattern. For arithmetic sequences, you add the common difference to the previous term to obtain the next term. Whereas, for geometric sequences, you multiply the previous term by the common ratio to find the next term. In general, term-to-term rules describe how to move from one term to another within the sequence.

Position-to-term rule: The value of a term is determined based on its position (term number) within the sequence, using a formula. This allows you to find any term directly without calculating all preceding terms.

Nth Term

The Nᵗʰ term of a sequence is a formula or expression that helps us find the value of any term in the sequence without having to list all the previous terms. It allows us to calculate the value of a term at a specific position (n) in the sequence.

Each type of sequence has a unique Nᵗʰ term formula that reflects its specific pattern or rule. By identifying the correct Nᵗʰ term formula for a given sequence, we can easily calculate the value of any term in the sequence. Also, we can better understand the relationships between the terms.

‘n’ in the Nᵗʰ term formula represents the position of the term in the sequence. When n = 1, we are looking for the first term in the sequence, and when n = 2, we are looking for the second term in the sequence.

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Last updated: April 15, 2022

This Privacy Policy describes Our policies and procedures on the collection, use and disclosure of Your information when You use our services. It also tells you about your privacy rights and how the law protects you.

We use Your Personal data to provide and improve our services. By using our services, you are agreeing to the collection and use of information in accordance with this Privacy Policy.

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Legal Basis for Processing Personal Data under GDPR

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In any case, we will gladly help to clarify the specific legal basis that applies to the processing, and in particular whether the provision of personal data is a statutory (required by law) or a contractual requirement, or a requirement necessary to enter into a contract.

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We may also limit how we collect, use, and store some of the information of users between 13 and 18 years old. In some cases, this means that we will be unable to provide certain functionalities of our services to these users. If we need to rely on consent as a legal basis for processing your information and your country requires consent from a parent, We may require the parent’s consent before we collect and use that information.

We may ask a user to verify their date of birth before collecting any personal information from them. If the user is under the age of 13, the service will either be blocked or redirected to a parental consent process.

Information Collected from Children Under the Age of 13

We may collect and store persistent identifiers, such as cookies or IP addresses from children, without parental consent for the purpose of supporting the internal operation of the our services.

We may collect and store other personal information about children if this information is submitted by a child with prior parental consent or by the parent or guardian of the child.

We may collect and store the following types of personal information about a child when submitted by a child with prior parental consent or by the parent or guardian of the child:

First and/or last name
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Parent’s or guardian’s name
Parent’s or guardian’s email address
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Parental Access

A parent who has already given the Company permission to collect and use their child’s personal information can, at any time:

Review, correct or delete the child’s personal information
Discontinue further collection or use of the child’s personal information
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Our Service may contain links to other websites that are not operated by us. If you click on a third party link, you will be directed to that third party’s site. We strongly advise you to review the privacy policy of every site you visit.

We have no control over and assume no responsibility for the content, privacy policies or practices of any third party sites or services.

Policies Unique to Our Tutoring Services

The following applies to students that have registered for our tutoring services and tutors and employees representing Shalom Education Ltd:

Your profile includes information such as your username and password, purchases or orders made by you, your interests, preferences, and feedback and survey responses.

Booking history including booking requests, subjects booked, set-up test while using our digital resources, any online meeting and recordings of your bookings

Electronic recordings from CCTV, tutoring session, video conference calls, communication history with other users, your interaction with Shalom Education Tutors, records of referral codes shared, redeemed and any promotions that have been applied to your account. All photo’s, videos and conference recordings may be used to protect learner’s, Tutors and employees and may be used as evidence to support any complaint.

Changes to this Privacy Policy

We may update Our Privacy Policy from time to time. We will notify You of any changes by posting the new Privacy Policy on this page.

We may let You know via email and/or a prominent notice on our website prior to the change becoming effective and update the “Last updated” date at the top of this Privacy Policy.

You are advised to review this Privacy Policy periodically for any changes. Changes to this Privacy Policy are effective when they are posted on this page.

Contact Us

If you have any questions about this Privacy Policy, You can contact us:

By email: info@shalom-education.com
By visiting this page on our website: https://www.shalom-education.com/contact
By phone number: 01206657616

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Last updated: December 27, 2022

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Thank you for choosing Shalom Education Tuition for your educational needs. These terms and conditions outline the rules and regulations for the use of our services, and the agreement that will govern your relationship with us.

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• Suspected fraud or illegal activity
• Cancelling your order

Any services that you purchase can only be returned in accordance with these terms and conditions. Our Returns Policy forms a part of these Terms and Conditions.

In general, you have the right to cancel your order and receive a full refund within 14 days of placing it. However, you cannot cancel an order for services that are made to your specifications or are clearly personalised, or for services that you have already received in part.

Money-Back Guarantee: If you are not satisfied with the quality of your tutoring session, you may be eligible for a full or partial refund or credit. To request a refund or credit, please contact us within 24 hours after the end of the session and provide a detailed explanation of your dissatisfaction. We will review your request and, if approved, will issue a refund or credit to your account.

Please note that refunds or credits may not be available for all types of tutoring services and may be subject to fees or other charges. For more information, please contact us.
Errors and inaccuracies
We strive to provide accurate and up-to-date information about the service we offer, but we cannot guarantee that everything will be completely accurate and up-to-date at all times. Prices, product images, descriptions, availability, and services may be inaccurate, incomplete, or out of date.

We reserve the right to change or update any information, and to correct errors, inaccuracies, or omissions at any time without prior notice.

Prices policy

We reserve the right to change our prices at any time before accepting your order.

Payments

All tutoring services and membership accounts purchased on our website must be paid for in full at the time of purchase, for the required time of use. We accept a variety of payment methods, including credit cards, debit cards, and online payment services like PayPal.

Your payment card may be subject to validation checks and authorisation by your card issuer. If we do not receive the necessary authorisation, we cannot be held responsible for any delays or failure to deliver your order.

Subscriptions

Subscription period

Our tutoring services are available with a pay-as-you-go option or a subscription option that is billed on a monthly or annual basis. The tutoring account subscription will end at the end of the period. You can choose the subscription option that best suits your needs and cancel at any time.

Our membership accounts are billed monthly or annually and do not automatically renew after the period. You can choose to renew your membership account at the end of the period if you wish to continue your membership.

Subscription cancellations

You can cancel your subscription renewal through your account settings or by contacting us. Please note that you will not receive a refund for fees you have already paid for your current subscription period, and you will be able to access the service until the end of your current subscription period.

Billing

We need accurate and complete billing information from you, including your full name, address, postal code, telephone number, and valid payment method. If automatic billing fails, you will not receive tutoring services until a payment is made. If payment is not made within a reasonable time period, your account may be terminated.

Fee changes

We reserve the right to modify the subscription fees at any time. Any change in fees will take effect at the end of your current subscription period.

We will give you reasonable notice of any fee changes so you have the opportunity to cancel your subscription before the changes take effect. If you continue to use the service after the fee change, you agree to pay the modified amount.

Refunds

In general, paid subscription fees are non-refundable. However, we may consider certain refund requests on a case-by-case basis and grant them at our discretion.

Free trial

We may offer free trials of our subscriptions at our discretion. You may be asked to provide billing information to sign up for a free trial. If you do provide billing information, you will not be charged until the free trial period ends.

On the last day of the free trial, unless you have cancelled your subscription, you will be automatically charged the applicable subscription fees for the plan you have chosen. We reserve the right to modify or cancel free trial offers at any time without notice.

Promotions

From time to time, we may offer promotions through the Service, such as discounts, special offers, or contests. These promotions may be governed by separate rules and regulations.

If you choose to participate in a promotion, please review the applicable rules and our privacy policy carefully. In the event of a conflict between the promotion rules and these terms and conditions, the promotion rules will take precedence.

Please note that any promotion may be modified or discontinued at any time, and we reserve the right to disqualify any participant who violates the rules or engages in fraudulent or dishonest behaviour. By participating in a promotion, you agree to be bound by the applicable rules and our decisions, which are final and binding in all matters related to the promotion.

User Accounts

In order to access certain features of our services, you may be required to create an account. When you create an account, you agree to provide accurate, complete, and current information about yourself as prompted by the account registration process. If you provide any false, inaccurate, outdated, or incomplete information, or if we have reasonable grounds to suspect that you have done so, we reserve the right to suspend or terminate your account.

You are solely responsible for maintaining the confidentiality of your account and password, and you agree to accept responsibility for all activities that occur under your account. If you believe that your account has been compromised or that there has been any unauthorised access to it, you must notify us immediately.

You may not use a username that is already in use by another user, that belongs to another person or entity without appropriate authorisation, or that is offensive, vulgar, or obscene. We reserve the right to remove or reclaim any username that we determine, in our sole discretion, to be inappropriate, infringing, or otherwise in violation of these terms and conditions.

Tutee Agreements

As a tutee using our service, you agree to the following terms and conditions:

• If you are under 18 years of age, you must have consent from a parent or guardian to register and that parent/guardian must enter into an agreement with Shalom Education to provide tuition services.
• You must contact a tutor through the Shalom Education tutoring platform. Any other means of communication is prohibited.
• You agree not to publish any abusive comments about a tutor or another tutee on the Shalom Education website or any other place. This includes defamatory or derogatory comments.
• You must not request a tutor to complete your coursework, essays, or other assignments given to you in your various schools but can request for support towards that.
• You agree not to make any agreement or arrangement with a tutor which is intended to circumvent the relationship between Shalom Education and the Tutor.

Expectations

• Lessons will be held at the frequency and duration agreed upon with us.
• Shalom Education will provide any necessary materials or resources for the lessons.
• You are expected to be punctual for lessons and to provide adequate notice for cancellations or rescheduling.
• You are expected to provide any necessary materials or resources for the lessons (e.g. pens, pencils or a protractor).

Responsibilities

• If you cancel a lesson less than 12 hours before the lesson is due to commence, you may be charged a cancellation fee of 50% of the lesson fee. If you cancel a lesson less than 2 hours before the scheduled start time of a lesson, you will be charged the full lesson fee.

Dispute Resolution
• If you have any concerns or issues with your tutoring experience, please contact us at tuition@shalom-education.com as soon as possible. We will work with you and your tutor to try to resolve any disputes or issues in a fair and reasonable manner.

Termination

• You may terminate your lessons with a tutor at any time by providing reasonable notice, as specified in your contract with us.

By using our service, you acknowledge that you have read and understand this agreement and agree to be bound by its terms. If you have any questions or concerns, please do not hesitate to contact us.

Copyright Policy

We respect the intellectual property rights of others and expect our users to do the same. It is our policy to respond to any claim that content posted on our service infringes the copyright or other intellectual property rights of any person.

If you are a copyright owner or authorised on behalf of one and you believe that your copyrighted work has been copied in a way that constitutes copyright infringement, please provide our copyright agent with the following information:

An electronic or physical signature of the person authorised to act on behalf of the owner of the copyright’s interests.
A description of the copyrighted work that you claim has been infringed, including the URL (web page address) of the location where the copyrighted work exists or a copy of the copyrighted work.
Identification of the URL or other specific location on our service where the material that you claim is infringing is located.
Your address, telephone number, and email address.
A statement by you that you have a good faith belief that the disputed use is not authorized by the copyright owner, its agent, or the law.
A statement by you, made under penalty of perjury, that the information in your notice is accurate and that you are the copyright owner or are authorised to act on the copyright owner’s behalf.
You may be held accountable for damages (including costs and attorneys’ fees) for misrepresenting that any content is infringing your copyright.

Upon receipt of a notification, we will take whatever action, in our sole discretion, we deem appropriate, including removal of the challenged content from our service. If you believe that your content has been removed in error, please contact us at queries@shalom-education.com.

Intellectual Property

The original content on our services (excluding content provided by you or other users), features, and functionality are and will remain the exclusive property of Shalom Education Ltd and its licensors. This includes, but is not limited to, text, graphics, images, logos, software, and other materials on our website and any proprietary technology used in the operation of our services.

Our service is protected by copyright, trademark, and other laws of both the United Kingdom and foreign countries. Our trademarks and trade dress may not be used in connection with any product or service without the prior written consent of Shalom Education Ltd. All other trademarks not owned by Shalom Education Ltd that appear on our service are the property of their respective owners.

By using our service, you acknowledge and agree that any intellectual property rights, including copyrights, trademarks, patents, and trade secrets, in the content and materials provided by Shalom Education Ltd or accessed through our service are the sole property of Shalom Education Ltd or the respective owners of such rights. You agree not to use, reproduce, modify, distribute, or create derivative works of such content and materials without the express written permission of Shalom Education Ltd or the respective owners of such rights.

You are responsible for protecting your own intellectual property rights and for obtaining any necessary licenses or permissions from the owners of any third-party intellectual property that you may use in connection with your use of our service. Shalom Education Ltd will not be liable for any claims or damages arising from your use of intellectual property that infringes the rights of others.

If you believe that your intellectual property rights have been violated on our service, please contact us at queries@shalom-education.com.

Your Feedback to Us

By submitting any feedback or suggestions to the company, you agree to assign to the company all rights, titles, and interests in such feedback or suggestions. If for any reason such assignment is ineffective, you agree to grant the company a non-exclusive, perpetual, irrevocable, royalty-free, worldwide right and license to use, reproduce, disclose, sublicense, distribute, modify, and exploit such feedback or suggestions without restriction.

You acknowledge that the company may use your feedback or suggestions for any purpose, including to improve the company’s products or services, and that the company is under no obligation to compensate you for your feedback or suggestions.

Links to Other Websites

Our Service may contain links to third-party websites or services that are not owned or controlled by Shalom Education Ltd. These links are provided for your convenience only and do not imply endorsement by our business of the linked website or service. We have no control over and assume no responsibility for the content, privacy policies, or practices of any third-party websites or services.

By using our Service, you acknowledge and agree that the use of any third-party websites or services is at your own risk. Shalom Education Ltd does not endorse or guarantee the accuracy or reliability of any content or materials on third-party websites or services, and we are not responsible for any errors or omissions.

In no event will Shalom Education Ltd be liable for any damage or loss caused or alleged to be caused by or in connection with the use of or reliance on any content, goods, or services available on or through any third-party websites or services. This limitation of liability applies to all claims.

We recommend that you carefully read the terms and conditions and privacy policies of any third-party websites or services that you visit, as they may differ from the terms and policies of our own services. If you have any concerns or questions about a third-party website or service linked from our service, we encourage you to contact the site or service directly for more information.

Termination

Shalom Education Ltd reserves the right to terminate or suspend your account at any time, without prior notice or liability, for any reason whatsoever, including but not limited to breach of these terms and conditions, fraudulent or illegal activity, or any other conduct that we deem inappropriate or harmful to our business or other users.

Upon termination, your right to use our services will immediately cease, and any outstanding balances or fees owed to Shalom Education Ltd must be paid in full. If you wish to terminate your account, you may simply stop using our services and contact us to request the closure of your account.

Any personal information or user-generated content associated with your account will be retained in accordance with our privacy policy, unless otherwise required by law.

You acknowledge and agree that Shalom Education Ltd will not be liable to you or any third party for any termination of your access to our services. You further agree that any rights or obligations that survive the termination of your account, such as indemnification or confidentiality obligations, will remain in effect.

“AS IS” and “AS AVAILABLE” Disclaimer

The service is provided to you “As is” and “As available” and with all faults and defects without warranty of any kind. While we make every effort to ensure the accuracy and reliability of our services, we cannot guarantee that they will be error-free or uninterrupted.

To the maximum extent permitted by applicable law, our business and its affiliates and licensors and service providers disclaim all warranties, expressed or implied, including but not limited to warranties of merchantability, fitness for a particular purpose, title and non-infringement. We do not make any representations or warranties that our services will meet your requirements, achieve any intended results, be compatible with any other software or services, operate without interruption, or be error-free.

We do not guarantee the accuracy, completeness, reliability, or timeliness of the information, content, or materials provided through our services.

We do not guarantee that our services or any content or materials provided through our services will be free from viruses, malware, or other harmful components. It is your responsibility to protect your device and system from such threats, and we recommend that you use appropriate security measures and virus protection software.

Some jurisdictions do not allow the exclusion of certain types of warranties or limitations on the applicable statutory rights of a consumer, so some or all of the above exclusions and limitations may not apply to you. In such cases, the exclusions and limitations set forth in this section shall be applied to the greatest extent enforceable under applicable law.

By using our services, you acknowledge and agree that your use is at your own risk, and that you are solely responsible for any damage or loss that may result from your use of our services.

Governing Law and Jurisdiction

These terms and your use of the service shall be governed by and construed in accordance with the laws of the country, excluding its conflicts of law rules. Any disputes arising out of or in connection with these terms or the use of the service shall be resolved through the courts of the country and you hereby consent to the exclusive jurisdiction of such courts.

Disputes Resolution

If you have any concerns or disputes related to the service, you agree to try to resolve the issue informally by contacting us first.

You can try contacting the company through email (queries@shalom-education.com) or by phone (01206657616) to see if we can come to an agreement or find a solution to your issue. This can be a quick and effective way to address any concerns or issues you may have, without the need for formal legal proceedings.

We will make every effort to address your concerns and reach a mutually satisfactory resolution. If we are unable to resolve the dispute informally, you may choose to bring the matter to alternative dispute resolution through a mediator or arbitrator. Any such alternative dispute resolution proceedings will be conducted in accordance with the laws of the country and will be confidential. You agree that any such dispute will be resolved on an individual basis and that class or collective actions are not permitted.

Severability and Waiver

Severability

If any provision of these terms and conditions is found to be invalid or unenforceable, that provision will be enforced to the maximum extent possible, and the remaining provisions will remain in full force and effect.

Waiver

The failure to exercise a right or to require the performance of an obligation under these terms and conditions shall not affect a party’s ability to exercise such right or require such performance at any time in the future. Similarly, the waiver of a breach of these terms and conditions shall not constitute a waiver of any subsequent breach.

Changes to These Terms and Conditions

We may update or change these terms and conditions at any time, at our sole discretion. If we make a material change to these terms, we will provide reasonable notice, such as by posting a notification on our website or through email, at least 30 days before the change takes effect. It is your responsibility to regularly check these terms and conditions for any updates or changes.

By continuing to access or use our Service after any updates or changes to these terms, you agree to be bound by the revised terms. If you do not agree to the updated or changed terms, in whole or in part, please stop using the website and our services.

Contact Us

If you have any questions about these terms and conditions, You can contact us:

By email: info@shalom-education.com
By visiting this page on our website: https://www.shalom-education.com/contact
By phone number: 01206657616

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