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) 3
B) 4
C) 2
D) 1
E) 7
Solution
Sum 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) = 9
Assuming r ^ 3 as x, we get
=> (x ^ 2 – 1) / (x – 1) = 9
=> (x ^ 2 – 1) = 9 (x – 1)
=> x ^ 2 – 9x + 8 = 0
=> x = 8
Thus r ^ 3 = 8, and r = 2
Common ratio of the series is 2
Correct Answer: C
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