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OCR GCSE Maths Arithmetic sequences

Arithmetic sequences

This page covers the following topics:

An arithmetic or linear sequence, an, is an ordered list of n numbers where the difference between each consecutive term, d, is constant. An arithmetic sequence can always be described by the general rule:

Basics of arithmetic sequences

The term to term rule of an arithmetic sequence describes how to get from one term to the next in the sequence. To find the term to term rule, subtract the first term from the second term to find the common first difference term. From the common first difference term and the first term the position to term rule, or general rule, can be worked out with the formula:

Generating terms in arithmetic sequences

The general rule of an arithmetic sequence can be used to work out the nth term of the sequence, the term at position n, and is given by the formula:

nth term of arithmetic sequences

A series is the sum of the terms of a sequence up to a certain number of terms and it is denoted by Sn. A series for an arithmetic sequence is given by the formula:

Arithmetic series

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What is the common difference term in the arithmetic sequence {UnΒ­} = {1, 17, 33, 49, 65, …, Un}?

OCR GCSE Maths Arithmetic sequences What is the common difference term in the arithmetic sequence {UnΒ­} = {1, 17, 33, 49, 65, …, Un}?
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2

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Katy notices that every six months her savings double in value. Is the sequence of savings at every six months period an arithmetic sequence?

OCR GCSE Maths Arithmetic sequences Katy notices that every six months her savings double in value. Is the sequence of savings at every six months period an arithmetic sequence?
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3

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Given the arithmetic sequence {anΒ­} = {1, 3, 5, 7, 9, 11, …, an}, find the common first difference term.

OCR GCSE Maths Arithmetic sequences Given the arithmetic sequence {anΒ­} = {1, 3, 5, 7, 9, 11, …, an}, find the common first difference term.
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4

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Given the first 7 terms of a sequence are {72, 84, 96, 108, 120, 132, 144}, what is the position to term rule, or general rule, of the sequence?

OCR GCSE Maths Arithmetic sequences Given the first 7 terms of a sequence are {72, 84, 96, 108, 120, 132, 144}, what is the position to term rule, or general rule, of the sequence?
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5

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Given the first three terms of a sequence are {24, 20, 16}, calculate the seventh term of the sequence.

OCR GCSE Maths Arithmetic sequences Given the first three terms of a sequence are {24, 20, 16}, calculate the seventh term of the sequence.
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6

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Define the nth term of the sequence {an} = {1, 3, 5, 7, 9, …, an}.

OCR GCSE Maths Arithmetic sequences Define the nth term of the sequence {an} = {1, 3, 5, 7, 9, …, an}.
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7

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Calculate the first 5 terms of the sequence anΒ­ = 3 – n.

OCR GCSE Maths Arithmetic sequences Calculate the first 5 terms of the sequence anΒ­ = 3 – n.
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8

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Jack notices that when he releases a red ball from a one-meter height, the number of bounces of the tennis ball increases by 2 with each 5 second interval. Given that during the first 5 second interval the ball bounced twice, what is the nth term of the sequence of bounces.

OCR GCSE Maths Arithmetic sequences Jack notices that when he releases a red ball from a one-meter height, the number of bounces of the tennis ball increases by 2 with each 5 second interval. Given that during the first 5 second interval the ball bounced twice, what is the nth term of the sequence of bounces.
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