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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
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+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

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