# How do you write an nth term rule for 5,10,20,40,... and find a_6?

Aug 7, 2016

${a}_{n} = 5 \times {2}^{n - 1} \text{ Note: NOT } {10}^{n - 1}$

#### Explanation:

This is a G.P. with a common ratio of 2, because each term is double the one before it. Finding the 6th term is really easy, we can simply double two more times to get 5, 10, 20, 40, 80, 160. But that it not what the question is all about. What if we had been asked for the 50th term?

The general term for any Term in a GP is ${a}_{n} = a {r}^{n - 1}$

We have $a$, the first term =5, and the common ratio $r$ = 2.

So, ${a}_{n} = 5 \times {2}^{n - 1}$ Note: NOT 10^(n-1)!!!