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.**