The sum of a geometric series is 127 and the sum of their reciprocals is 127/64. The first term is 1. Find the number of terms and common ratio.
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Answer:
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
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