SOLUTION: In a geometric progression, the 2nd term is 8 and the 7th term is .25. Find the sum of the first 10 terms.

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Question 925143: In a geometric progression, the 2nd term is 8 and the 7th term is .25. Find the sum of the first 10 terms.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
First term, a.
Index, n.
ratio between terms, r.
a%2Ar=8, also a%2Ar%5E%282-1%29=8 or a%2Ar%5E%28n-1%29=TheGeneralTerm.

The seventh term, ar%5E%287-1%29=0.25.
a%2Ar%5E6=0.25

Two equations should be useful.
system%28ar=8%2Car%5E6=%281%2F4%29%29

Their ratio should be very helpful.
%28ar%5E6%29%2F%28ar%29=%281%2F4%29%2F8
r%5E5=1%2F32
r%5E5=1%2F2%5E5
r%5E5=%281%2F2%29%5E5
highlight%28r=1%2F2%29

Having the common ratio, the factor a can be found.
a%2A%281%2F2%29=8
a=16

The general term of the geometric sequence is highlight%2816%2A%281%2F2%29%5E%28%28n-1%29%29%29.

If the formula for a finite series is being handled properly, expect sum of first ten terms,
16%281-%281%2F2%29%5E10%29%2F%281-1%2F2%29, and you can evaluate the expression.

16%281-1%2F1024%29%2A2

and this is slightly less than 32.