SOLUTION: The third term of a geometric progression is nine times the first term. The sum of the first six terms is k times the sum of the first two terms. Find the value of k.
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Question 1202408: The third term of a geometric progression is nine times the first term. The sum of the first six terms is k times the sum of the first two terms. Find the value of k. Answer by ikleyn(52925) (Show Source):
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The third term of a geometric progression is nine times the first term.
The sum of the first six terms is k times the sum of the first two terms. Find the value of k.
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= + + + + + .
Group the terms
= () + () + ().
You are given = .
It implies = ; = ; = .
Therefore
= + + = = .
Thus the coefficient k is equal to 91.
ANSWER. k = 91.
