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Question

Let a1,a2,a3,.... be terms of an A.P.
If a1+a2+....+apa1+a2+.....+aq=p2q2,pq then a6a21 must be-

A
Less than 1
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B
27
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C
1141
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D
72
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Solution

The correct options are
A Less than 1
D 1141
Given a1+a2+a3+...+apa1+a2+a3+...+aq=p2q2
p2[2a1+(p1)d]q2[2a1+(q1)d]=p2q2
2a1+(p1)d2a1+(q1)d=pq
2a1q+(p1)qd=2a1p+(q1)pd
2a1(pq)=(pqqqp+p)d
d=2a1
So, a6a21=a1+5da1+20d
=a1+10a1a1+40a1
=11a141a1
=1141

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