Question

How do you write the expression for the nth term of the geometric sequence `a_1=100, r=e^x, n=9`?

Answer 1

`n^(th)term=a_n=100(e^x)^(n-1)`
But
`9^(th)term=a_9=100(e^x)^8`

Explanation:

The `n^(th)`term of the geometric sequence is :

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

Given that ,

`a_1=100,r=e^x and n=9`

`:.n^(th)term=a_n=100(e^x)^(n-1)`

`:.9^(th)term=a_9=100(e^x)^(9-1)=100(e^x)^8`