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in Geometric Progressions by (15.9k points)

The sum of an infinite geometric series is 20, and the sum of the squares of these terms is 100. Find the series.

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1 Answer

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Given: \(\frac{a}{1-r} = 20\) & \(\frac{a^2}{1-r^2}\) = 100

(Because on squaring both first term a and common ratio r will be squared.)

To find: the series

a = 20(1-r) ...... (1)

Put this value of r in equation (i) we get

∴The infinite geometric series is:8, \(\frac{24}{5}, \frac{72}{25}, \frac{216}{125}, \frac{648}{625}, .... \infty\)

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