# Arithmetic Sequences

## An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.

##### MatchsticksLevel 1Level 2Level 3Level 4Exam-StyleDescriptionHelpMore

This is level 3: find a given term of these linear sequences. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

 Find the 18th term of the linear sequence that begins: 8, 14, 20, 26. Find the 29th term of the linear sequence that begins: 17, 24, 31, 38. What is the one hundredth term of the arithmetic sequence that begins:11, 17.5, 24, 30.5? Find term number 10 of the sequence: 5, 12, 19, 26, 33, 40, ... Find term number 24 of the sequence: 7, 12, 17, 22, 27, 32, ... Find term number 22 of the sequence: 9, 1, -7, -15, -23, -31, ... Find term number 22 of the sequence: -8, -1, 6, 13, 20, 27, ... Find term number 38 of the sequence: -0.8, -1.6, -2.4, -3.2, -4, -4.8, ... The second term of an arithmetic sequence is 15 and the sixth term is 39. Find the tenth term. The third term of an arithmetic sequence is 19.6 and the seventh term is 44.8. Find the twentieth term.
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This is Arithmetic Sequences level 3. You can also try:
Matchsticks Level 1 Level 2 Level 4 Geometric Sequences

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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#### Number Crunch Saga

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Sarah Murphy, Teacher

Monday, February 26, 2024

"For level 2 of this activity, it's not clear how the answer needs to be entered. In the help notes they make reference of things with subscripts. Guidance of the format to enter for the answer is needed.

[Transum: Thanks for your feedback Sarah. For level 2 the answer should be typed in as an expression (no equals sign) in its simplest form. For example, an answer might be '7n' or '5n-2'. No subscripts are required.]"

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## Description of Levels

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Matchsticks - A beginner's exercise that lets you see how a sequence is structured.

Level 1 - Find the next term of these linear sequences

Level 2 - Find the nth term of these linear sequences

Level 3 - Find a given term of these linear sequences

Level 4 - Mixed questions about linear sequences and their sums

Missing Terms - Find the missing terms of arithmetic, geometric and Fibonacci-type sequences in this self marking quiz.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Geometric Sequences - A similar exercise on geometric sequences.

Sigma - Practise using the sigma notation to find the sum of various number series.

More on this topic including lesson Starters, visual aids and investigations.

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## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Arithmetic Sequences

Here is a reminder of some facts that may help you answering the questions in this exercise.

An arithmetic sequence, sometimes called an arithmetic progression, is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 8, 11, 14, 17, 20, 23, . . . is an arithmetic sequence with common difference of 3.

The first term of the sequence can be written as u1

The nth term of the sequence can be written as un

The common difference is usually written as d

The formula for finding the nth term is un=u1+(n-1)d

The formula for finding the sum of n terms is Sn=½n(2u1+(n-1)d)

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