The sum of the first nth term of a geometric progression is 127 and the sum of their reciprocal is 127/64. The first term is 1. Find n and the common ratio.

Answer 1

Sn = a(1-r^n)/(1-r), so

127 = 1(1-r^n)/(1-r)

127/64 = 1(1-1/r^n)/(1-1/r)
= r^(1-n)(1-r^n)/(1-r)

dividing, we get

1/64 = r^(1-n)
or,
r^(n-1) = 64

1+2+4+8+16+32+64 = 127

Looks like r=2,n=7

Answer 2

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