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  • If for an A.P., aq = q and aq = p, then value of ap+q isOption: 1 1<div class='qna-opti

If for an A.P., aq = q and aq = p, then value of ap+q is

Option: 1

1


Option: 2

0


Option: 3

3


Option: 4

None of these


Answers (1)

best_answer

Let the first term be a and common difference be d

So,

a_p=q\Rightarrow a+(p-1)d=q            ...........(1)

and 

a_p=q\Rightarrow a+(q-1)d=p                        ..........(2)

(2) - (1) ,

(q-1)d-(p-1)d=p-q

\Rightarrow (q-p)d=(p-q)

\Rightarrow d=-1

Putting d = -1 in (1),

a+1 -p=q\Rightarrow a=p+q-1

So, a_{p+q}= a+(p+q-1)d

a_{p+q}= a+(p+q-1)-(p+q-1)

a_{p+q}= 0

Posted by

shivangi.shekhar

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