Question

How many terms are there in a geometric series if the first term is 3, the common ratio is 4, and the sum of the series is 1,023?

Answer 1

In Geometric Progression, we know S(n) = a.(rⁿ - 1 ) / r - 1
Here, a = 3, r = 4 a(n) = 1,023
1023 = 3 (4ⁿ - 1) / (4 - 1)
3(4ⁿ - 1) = 1023 * 3
4ⁿ - 1 = 3069 / 3
4ⁿ = 1023 + 1
4ⁿ = 1024
4⁵ = 1024

In short, Your Answer would be 5 Terms

Hope this helps!