Geometric Series Question

Question

find the indicated term for the geometric series:

S_n=165, a_n = 48, r = -2/3; a₁

Answer 1

There's actually enough information to answer the question, it's just a bit weird.  Since we're given the nth term of the series, we can work backwards to find the others that came before it. 

The ratio to find the next term in this series is -2/3, so to find the previous term we want to multiply by -3/2 instead.  Using this technique we can see that the n-1st term is -72, and so on down the line.  It shouldn't take too long before you reach the first term of the series which you know is the right one because when you add up all the terms you've found so far, you get a sum of 165.