# Thread: Infinite geometric sequence question

1. ## Infinite geometric sequence question

The second term of an infinite geometric sequence is 4/9, and the sixth term is 9/64.

What is the sum of the first five terms of this sequence?

What is the sum of all off the terms of this sequence?

2. Hello,
Originally Posted by cityismine
The second term of an infinite geometric sequence is 4/9, and the sixth term is 9/64.

a_2=4/9
a_6=9/64

we also know that a_6=a_2*q^4, where q is the constant progression.

Then a_6/a_2=81/256=q^4 and :

q=+ or - 3/4

Is it enough for you to continue ? (there are 2 possible answers to the following questions ^^)

3. Also, you're probably gonna need this:
Sum of a geometric series:

Sum of an infinite geometric series:

Also, to find t_1, just remember that:

Like, for instance:

4. Thanks, I was able to take it from there and solve it. The answers I got are 781/432 and 27/64. They match the ones in the back of the book.