Finding The Nth Term Using The Zero Term

You can work our the nth term to a sequence by finding the zero term as follows :

As an example , using the below sequence:

3 , 9, 15, 21, 27 …….

The difference between the above terms is 6, so the zero term to this sequence would be 6n-3, so if I wanted to find any term in this sequence, such as the 6th term, this would be 6x6-3= 33. As a check, we know the 5th term to this sequence is 27, so the next number in the sequence would be 27 + 6 which is 33.

You can work out any number in the sequence using the above nth term.

You can also use the nth term to see if a number is actually in the sequence, ie 87

You can write the equation 6n-3=87, therefore 6n= 87 + 3 =90. 90 will be the 15th term in the above sequence.

119 would not be in the sequence as using the above equation 6n-3=119, 6n would equal 122, which would be 20.33, not an integer.

You can also use the above method for working out negative terms such as 9n-41, being the zero term, so the 8th term in this sequence would be 8 x 9=72 -41=31 and the 30th term would be 30 x 9 -41 = 229

-32 , -23, -14, -5, 4, 13 ……

This is a very easy and quick way of working out the nth term without have to write out the tables below each term .