# Sequence and Series

 Categories : Sequence and Series The sum of the first 6 terms of a geometric sequence is 9 times the sum of its first 3 terms. Find the common ratio.A)    3B)    4C)    2D)    1E)    7SolutionSum of n terms of a geometric series is given by a ( r^n – 1) / r – 1    where a, r and n are the first term, ratio and number of terms of the series respectively.Plugging in values, we get, => (a (r ^ 6 – 1) / r – 1) / (a (r ^ 3 – 1) / r – 1) = 9=> (r ^ 6 – 1) / (r ^ 3 – 1) = 9Assuming r ^ 3 as x, we get=>  (x ^ 2 – 1) / (x – 1) = 9=>  (x ^ 2 – 1) = 9 (x – 1) =>  x ^ 2 – 9x + 8  = 0=>  x = 8Thus r ^ 3 = 8, and r = 2Common ratio of the series is 2Correct Answer: CAbout the Author...

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