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Question

If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is


A

- p

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B

p

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C

p + q

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D

p - q

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Solution

The correct option is B

p


As, ap=q

a+(p1)d=q(i)

Also, a(p+q)=0

a+(p+q1)d=0(ii)

Subtracting (i) from (ii), we get

a + (p + q - 1)d - a - (p - 1)d = 0 - q

(p+q1p+1)d=q

qd=q

d=qq

d=1

Substituting d = - 1 in (i) we get

a+(p1)×(1)=q

ap+1=q

a=p+q1

Now,

aq=a+(q1)d

=p+q1+(q1)×(1)

=p+q1q+1

=p

Hence, the correct alternative is option (b).


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