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Statement -1: If a(1),a(2),a(3), . . . ....

Statement -1: If `a_(1),a_(2),a_(3), . . . . .,a_(n), . . .` is an A.P. such that `a_(1)+a_(4)+a_(7)+ . . . .+a_(16)=147`, then `a_(1)+a_(6)+a_(11)=98`
Statement -2: In an A.P., the sum of the terms equidistant from the beginning and the end is always same and is equal to the sum of first and last term.

A

Statement -1 is true, Statement -2 is True, Statement -2 is a correct explanation for Statement for Statement -1.

B

Statement -1 is true, Statement -2 is True, Statement -2 is not a correct explanation for Statement for Statement -1.

C

Statement -1 is true, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

Verified by Experts

The correct Answer is:
A
Statement -2 is a property of an A.P. So, it is true.
Now, `a_(1)+a_(4)+a_(7)+ . . . .+a_(16)=147`
`rArr" "(a_(1)+a_(16))+(a_(4)+a_(13))+(a_(7)+a_(10))=147`
`rArr" "3(a_(1)+a_(16))=147" [Using statement -2]"`
`rArr" "a_(1)+a_(16)=49`
`:." "a_(1)+a_(6)+a_(11)+a_(16)`
`=(a_(1)+a_(16))+(a_(6)+a_(11))=2(a_(1)+a_(16))=2xx49=98`
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