Question

What is the nth term of the geometric sequence 2,10,50,250?

Answer 1

Use the explicit formula for a geometric sequence:

`a_n=a_1(r)^(n-1)`

Explanation:

First, find the common ratio `r=10/2=5`

Now, insert the values from the problem into the explicit formula ...

`a_n=2(5)^(n-1)`

So, for example if you want to know the 11th term ...

`a_11=2(5)^((11-1))=19,531,250` [wow! that's a big number!]

Hope that helped!