# 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 10th term of the linear sequence that begins: 8, 16, 24, 32. Find the 27th term of the linear sequence that begins: 15, 20, 25, 30. What is the one hundredth term of the arithmetic sequence that begins:16, 23.5, 31, 38.5? Find term number 16 of the sequence: 4, 9, 14, 19, 24, 29, ... Find term number 20 of the sequence: 6, 14, 22, 30, 38, 46, ... Find term number 22 of the sequence: 6, 0, -6, -12, -18, -24, ... Find term number 21 of the sequence: -7, 0, 7, 14, 21, 28, ... Find term number 22 of the sequence: -0.8, -1.9, -3, -4.1, -5.2, -6.3, ... The second term of an arithmetic sequence is 13 and the sixth term is 41. Find the tenth term. The third term of an arithmetic sequence is 22.6 and the seventh term is 51.8. 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

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#### ChrisMaths

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## Teachers

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/Maths/Exercise/Sequences/Arithmetic.asp?Level=3

## 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.

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)

The excellent video above is from Corbettmaths.

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