# How do you write a rule for the nth term of the geometric sequence given the two terms #a_2=36, a_4=576#?

##### 1 Answer

May 16, 2017

See explanation.

#### Explanation:

For any geometric sequence

#a_n=a_k*q^(n-k)#

In this task we can write that:

#576=36q^2#

This leads to 2 possible values of

Now we can calculate the first term separately for

If

else if

So this task has 2 solutions: