SOLUTION: The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)...

Question 142025: The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)...
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)...
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a(4) = ar^3 = 56
a(6) = ar^5 = (7/8)
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Divide a(6) by a(4) to get:
r^2 = 1/64
r = 1/8
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Substitute to find a(1):
a(1/8)^3 = 56
a = 56/(1/8)^3 = 28672
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GP: 28672, 28672(1/8), 28672(1/8)^2 etc
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S(n) = a[1-(r^n)]/[1-r]
Since 0 S(n) = a/[1-r] = 28672/[1-(1/8)] = 32768
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Cheers,
Stan H.
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