SELECT * FROM question_mgmt as q WHERE id=1067 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=2 AND subId=6 AND chapterId=80 and ex_no='5' AND status=1 ORDER BY CAST(question_no AS UNSIGNED)

Question:

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

Answer:

Let the G.P. be T1, T2, T3, T4, … T2n.

Number of terms = 2n

According to the given condition,

T1 + T2 + T3 + …+ T2n = 5 [T1 + T3 + … +T2n–1]

⇒ T1 + T2 + T3 + … + T2n – 5 [T1 + T3 + … + T2n–1] = 0

⇒ T2 + T4 + … + T2n = 4 [T1 + T3 + … + T2n–1]

Let the G.P. be a, ar, ar2, ar3, …

therefore space fraction numerator a r space open parentheses r to the power of n space minus 1 close parentheses over denominator r minus 1 end fraction space equals space fraction numerator 4 space cross times space a open parentheses r to the power of n space minus 1 close parentheses over denominator r space minus 1 end fraction rightwards double arrow a r space equals space 4 a rightwards double arrow r space equals space 4

Thus, the common ratio of the G.P. is 4.


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