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If a(1),a(2),….a(50) are in GP, then (...

If `a_(1),a_(2),….a_(50)` are in GP, then ` (a_(1)-a_(2)+a_(5)-....+a_(49))/(a_(2)-a_(4)+a_(6)-....+a_(50))` is

A

0

B

1

C

`(a_(1))/(a_(2))`

D

`(a_(25))/(a_(24))`

Text Solution

Verified by Experts

The correct Answer is:
c
Let `a_(2) = ra_(1),a_(3) = r^(2)a_(1),…, ` so on
` :. (a_(1) -a_(3) +a_(5)- ....+a_(49))/(a_(2)-a_(4)+a_(6)-...+a_(50)) = (a_(1)-r^(2)a_(1)+r^(4)a_(1)-...r^(48)a_(1))/(a_(1)r-r^(3)a_(1)+r^(5)a_(1)- ... + r^(49)a_(1))`
` (a_(1)(1-r^(2)+r^(4)-...+r^(48)))/(a_(1)r(1-r^(2)+r^(4)-...+r^(48)))1/r = (a_(1))/(a_(2))`
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