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The sum of the series a-(a+d)+(a+2d)-(a+...

The sum of the series `a-(a+d)+(a+2d)-(a+3d)+...` up to `(2n+1)` terms is: a. `-n d`. b. `a+2n d`. c. `a+n d`. d. `2n d`

A

`-nd`

B

a+2nd

C

a+nd

D

2nd

Text Solution

Verified by Experts

The correct Answer is:
C
The given series is an AGP with common ratio-1.
S=a-(a+b)+(a+2d)-(a+3d)+ . . . .+(a+2nd)
`rArr" "-S=-a+(a+d)-(a+2d)+ . . . .+(a+(2n-1)d)-(a+2nd)`
`:." "2S=a+{-d+d-d+d . . .` upto 2n terms}+(a+2nd)
`rArr" "2S=2a+2ndrArrS=a+nd`
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Section I - Solved Mcqs
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