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

Guest Mar 13, 2017

#1**+5 **

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**

Guest Mar 13, 2017