First and last term of a geometric progression are 3 and 96. If sum of these terms is 189, then find number of terms?

Question

First and last term of a geometric progression are 3 and 96. If the sum of all these terms is 189, then find the number of terms in this progression.

Answer 1

189 - ( 3 + 96 ) = 90 { sum of the remaining terms }
96/3 = 32 =======> r^(x) r - common multiple, x - integer that represents the number of terms available in the series.
this implies 32 is divisible by r. Starting from the lowest possible r that fulfills this condition we can check for answer by trial and error.
case 1: r=2
3 + 3*2 + 3*4 + 3*8 + 3*16 + 3*32 = 189
which is also the given sum hence the number of terms in the given series is 6.