The Nth Term of a Number Sequence Help (Increasing Linear Sequences)

The formula of a number sequence is known as the nth term. This formula tells you how to get from the position number (n) of the sequence to the number in the sequence. Follow these steps to find the nth term:

Step A First write the position numbers (1 to 5) above your sequence. Leave some space between them.

Step B Work out what the sequence is going up in, and multiply all your position numbers by this number. Put this in the space you have left.

Step C Work out what you have to add/take to these numbers to give the numbers in the sequence.

Step D Write down you nth term by putting the number you multiplied by before n (the answer from step B) and the number you had to add or take away at the end of your formula (the answer from step C)

Example 1

Find the nth term of this number sequence 7, 10, 13, 16, 19...

Step A First write the position numbers (1 to 5) above your sequence. Leave some space between them.

1              2              3              4              5              n

7             10            13            16            19

Step B Work out what the sequence is going up in, and multiply all your position numbers by this number. Put this in the space you have left.

To get the next number in your sequence you add on 3, so multiply all the position numbers by 3.

1              2              3              4              5              n

3              6              9             12            15             3n

7             10            13            16            19

Step C Work out what you have to add/take to these numbers to give the numbers in the sequence.

To get the numbers in the sequence you need to add on 4 to the multiples of 3.

Step D Write down you nth term by putting the number you multiplied by before n (the answer from step B) and the number you had to add or take away at the end of your formula.

nth term = 3n + 4

For an alternative approach to working out the nth term then click here.