Arithmetic Sequences

An arithmetic sequence, also known as an linear sequence, is a series of numbers where the difference between the numbers remains constant. Pupils may be asked to work out the nth term of a sequence in their GCSE examination.

There are some simple steps a student could use to work out the nth term of a sequence:

1. Write out the difference between each pair of terms.
2. Then work out the zero term of the sequence by subtracting difference from first term.
3. Lastly, write down the formula that corresponds to the nth term, remembering to substitute the values that you found for the difference and the zero term.

Worked example

The following are the first five terms of an arithmetic sequence

2,6,10,14,18

To find an expression for the nth term we look for the difference between each pair of numbers. In this case the difference is 4. We then proceed to find the zero term which for our sequence is 2-4=-2.

Expressing in term of the nth term leads to 4n-2, which is our answer.