A G.P CONSISTS OF EVEN NUMBER OF TERMS. IF THE SUM OF ALL THE TERMS IS 5 TIMES THE SUM OF TERMS OCCUPYING ODD PLACES ,THEN FIND THE COMMON RATIO

Asked by PAWANDEEP KAUR | 15th Nov, 2010, 06:26: PM

Expert Answer:

Dear Student,

Let there be n terms.

a, ar, ar2, ar3,……………..arn-2, arn-1

The sum of a G.P. = a[rn-1]/(r-1)

Odd terms of the sequence are:

a, ar2, ar4……………..arn-2

So sum of this series = a[(r2)n/2-1]/(r2-1)

=> a [rn-1]/(r2-1)

According to given problem:

a[rn-1]/(r-1) = 5 × a[rn-1]/(r2-1)

=> 1/(r-1) = 5/(r2-1)

=> 1/(r-1) = 5/[(r-1)×(r+1)]

=> r+1 = 5………………. (Because r cannot be equal to 1)

=> r = 4

Regards Topperlearning.

Answered by  | 15th Nov, 2010, 07:26: PM

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