Find r in a GS if the first term is 2/3 and the 7th term is 128/2187

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Find r in a GS if the first term is 2/3 and the 7th term is 128/2187?

Guest Jun 17, 2015

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Best Answer

The n'th term in a geometric series is a*r^(n-1)where a is the first term; so:

$$\frac{2}{3}r^6=\frac{128}{2187}$$

or

$$r=(\frac{3*128}{2*2187})^\frac{1}{6}=(\frac{64}{729})^\frac{1}{6}=\frac{2}{3}$$

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Alan Jun 17, 2015

Alan · Answer 1 · 2015-06-17T09:41:11

The n'th term in a geometric series is a*r^(n-1)where a is the first term; so:

$$\frac{2}{3}r^6=\frac{128}{2187}$$

or

$$r=(\frac{3*128}{2*2187})^\frac{1}{6}=(\frac{64}{729})^\frac{1}{6}=\frac{2}{3}$$

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