Nth Term Of A Sequence - GCSE Maths - Third Space Learning

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What is the nth term?

The nth term is a formula that enables us to find any term in a sequence. It refers to the position of a term in a sequence. For example, the first term has n=1, the second term has n=2, the 10th term has n=10 and so on. The ‘n’ stands for its number in the sequence.

We can make a sequence using the nth term by substituting different values for the term number(n).

To find the 20th term we would follow the sequence formula but substitute 20 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.

For example if the nth term = 2n + 1

  • To find the first term we substitute n = 1 into the nth term.

1st term = 2(1) + 1 = 3

  • To find the second term we substitute n = 2 into the nth term.

2nd term = 2(2) + 1 = 5

  • To find the third term we substitute n = 3 into the nth term.

3rd term = 2(3) + 1 = 7

  • To find the tenth term we substitute n = 10 into the nth term.

10th term = 2(10) + 1 = 21

Below are a few examples of different types of sequences and their nth term formula.

Type of Sequence Example nth Term
Arithmetic 6, 2, -2, -6, -10, ...10-4n
Geometric 1, 2, 4, 8, 16, 32, ...2^{n-1}
Quadratic3, 9, 19, 33, 51, ... 2n^{2}+1
Cubic2, 22, 78, 188, 370, ...3n^{3}-n

In this lesson, we will look specifically at finding the nth term for an arithmetic or linear sequence.

What is the nth term?

What is the nth term?

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