+60 How many terms are there in a geometric series if the first term is 3, the common ratio is 2, and the sum of the series is 93? Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio
+128406 How many terms are there in a geometric series if the first term is 3, the common ratio is 2, and the sum of the series is 93?
Sum = a1 [ 1 - r^n] / [ 1 -r ] where a1 is the first term, n is the number of terms and r is the common ratio
93 = 3 [ 1 - 2^n ] / [ 1 - 2] simplify.......divide both sides by 3
31 = [1-2^n] / -1 multiply the fraction on the right by -1 on top/bottom
31 = 2^n - 1 add 1 to both sides
32 = 2^n and we can write 32 as 2^5
2^5 = 2^n
So......n = 5 terms
