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# AQA GCSE Maths Arithmetic sequences

1. Basics of arithmetic sequences
2. Generating terms in arithmetic sequences
3. nth term of arithmetic sequences

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:

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:

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:

# 1

Find the common first difference term of the sequence {an} = {1, 17, 33, 49, 65, 81, …, an}.

# 2

Given an arithmetic sequence with the first two terms a₁ = 72 and a₂ = 4, find the general rule describing the sequence.

# 3

Louise is part of her school’s football team. She notices that with each training session the number of keepie uppies she can do increases by 7. Given she could do 2 keepie uppies in her first training session, how many will she be able to do on her twelfth training session?

# 4

Is the sequence Un = 14n – 7 an example of an arithmetic sequence?

# 5

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

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