CBSE Class 11-science Answered
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 | 15 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 | 15 Nov, 2010, 07:26: PM
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