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Question

Let a1,a2,a3,... be the terms of an A.P. If a1+a2+...+apa1+a2+...+aq=p2q2; pq, then a6a21 is equal to

A
4111
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B
72
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C
27
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D
1141
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Solution

The correct option is D 1141
Given : a1+a2+...+apa1+a2+...+aq=p2q2
p2[2a1+(p1)d]q2[2a1+(q1)d]=p2q22a1+(p1)d2a1+(q1)d=pq[2a1+(p1)d]q=[2a1+(q1)d]p2a1(qp)=d[(q1)p(p1)q]2a1=d

a6a21=a1+5da1+20d =a1+10a1a1+40a1 =1141

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