What is the sum of the first five terms of a geometric series with a1 = 20 and r = 1/4?

Question

Mathematics

Zayden

19 October, 21:58

What is the sum of the first five terms of a geometric series with a1 = 20 and r = 1/4?

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Schroeder · Answer 1

Sum of the first n terms of a geometric sequence is Sn = a (1 - r^n) / (1 - r)

Sn = 20 (1 - (1/4) ^5) / (1 - 1/4) = 20 (1 - 1/1024) / (3/4) = 20 (1023/1024) / (3/4) = 26 41/64