How many terms are there in a geometric series if the first term is 5, the common ratio is 2, and the sum of the series is 315?
Hint: r ≠ 1, where a1 is the first term and r is the common ratio.
n = 3 n = 4 n = 5 n = 6
Sum =F x [1 - R^N] / [1 - R]
315 = 5 x [1 - 2^N] / [1 - 2]
Solve for N over the real numbers:
315 = 5 (2^N - 1)
315 = 5 (2^N - 1) is equivalent to 5 (2^N - 1) = 315:
5 (2^N - 1) = 315
Divide both sides by 5:
2^N - 1 = 63
Add 1 to both sides:
2^N = 64
64 = 2^6:
2^N = 2^6
Equate exponents of 2 on both sides:
Answer: |N = 6
