## Unit Digit Shortcut

### Suppose you have a series

P, Q, R, S ,T, P, Q, R, S ,T,P, Q, R, S ,T,P, Q, R, S ,T,P, Q, R, S , T,P, Q, R, S, T …..

And you have to find out the 16 ^{th} term of the series. How would you do this?

One way to solve this is by counting the 16 ^{th} term; you get your answer P.

The other way to solve : You can divide the 16 by 5 and get the remainder as 1. So now answer would be the 1 ^{st} term that is P.

Why we have divided by 5 because the terms in the series are repeated after a cycle of 5.

### Let us take another question.

Find out the 25 ^{th} term of the above series. Following the same procedure you get

25/ 5 gives you the remainder zero (0)

In such case, your answer should be the last term of the cycle and the last term of the cycle is T

25^{th} term is T.