# Maths Geometric Series, Got a test in half an hour!

Ok here is the question

A geometric series has ten terms. The first one being 0.125 and the last one being 64. Calculate the common ratio.

Rig:

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So s1 = .125, s2 = .125r, ..., s10 = .125r^10=64.

Thus r = (64/.125)^(1/10)

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Quote by Negative Burn
So s1 = .125, s2 = .125r, ..., s10 = .125r^10=64.

Thus r = (64/.125)^(1/10)

That isn't calculus, that's just sense. Also the final term is

.125 * r^9 = 64,

because there's 10 total terms and the first is r^0.

May help if you recognize that 64 is 2^6 and .125 is 2^-3. So r = (2^6/2^-3)^(1/9), which simplifies to 2. So the common ratio is 2.
Quote by Meths
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the formula for sum of terms of a GP is:
Sn = a(1-r^n) / (1-r)

where a = first term,
r = common ratio.

Sub in the values.
Sn = 64
a=0.125
n=10,

and you can find r
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