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.
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, …
Thus, the common ratio of the G.P. is 4.
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6 Comment(s) on this Question
Thank u it was very helpfull
Its Helpful
Yes the process is correct and the answer as well,but there is a mistake.If it is taken that the original g.p is a,ar^2,a^3... the common ratio between the odd terms and even terms should be r^2.
Thank u
Thank you
it was very helpful!!!!
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