Question

How do you write a formula for the general term (the nth term) of the geometric sequence 4, 12, 36, 108, 324, . . .?

Answer 1

`x_n=4*3^(n-1)`

Explanation:

The general term of any geometric sequence `(x_n)` is given by

`x_n=ar^(n-1)`, where `a` is the first term and `r` is the common ratio defined as `r=x_(n+1)/x_n`.

So in this case `a=4` and `r=21/4=3`.

`therefore x_n=4*3^(n-1)`