Hi guys, need help with this question please:

The first term of a geometric series is 8. The sum of its first 10 terms is 1/8 of the sum of the reciprocal of these terms. Find the common ratio.

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- Jun 22nd 2011, 02:52 AMBlizzardyGeometric Progression
Hi guys, need help with this question please:

The first term of a geometric series is 8. The sum of its first 10 terms is 1/8 of the sum of the reciprocal of these terms. Find the common ratio. - Jun 22nd 2011, 02:58 AMmr fantasticRe: Geometric Progression
- Jun 22nd 2011, 07:29 PMBlizzardyRe: Geometric Progression
- Jun 22nd 2011, 07:59 PMmr fantasticRe: Geometric Progression
You have $\displaystyle \frac{8(1 - r^{10})}{1 - r} = \frac{1}{64} \frac{1 - \frac{1}{r^{10}}}{1 - \frac{1}{r}}$

My advice is to multiply the numerator and denominator of the right hand side of this equation by r^10. Then factorise the denominator, then look for common factors to cancel, simplify etc.

I end up with the simple equation $\displaystyle r^9 = - \frac{1}{8^3}$