Let a1,a2,a3,.... be terms of an A.P. If a1+a2+....+apa1+a2+.....+aq=p2q2,p≠q 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 D1141 Given a1+a2+a3+...+apa1+a2+a3+...+aq=p2q2 ⇒p2[2a1+(p−1)d]q2[2a1+(q−1)d]=p2q2 ⇒2a1+(p−1)d2a1+(q−1)d=pq ⇒2a1q+(p−1)qd=2a1p+(q−1)pd ⇒2a1(p−q)=(pq−q−qp+p)d ⇒d=2a1 So, a6a21=a1+5da1+20d =a1+10a1a1+40a1 =11a141a1 =1141