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If a1, a2, a3, be terms of an A.P. if (...

If `a_1, a_2, a_3, ` be terms of an A.P. if `(a_1+a_2+...+a_p)/(a_1+a_2+...+a_q)=(p^2)/(q^2), p!=q ,t h e n(a_6)/(a_(21))` equals

A

`(41)/(11)`

B

`(7)/(2)`

C

`(2)/(7)`

D

`(11)/(41)`

Text Solution

Verified by Experts

The correct Answer is:
D
`:.((p)/(2)[2a_(1)+(p-1)d])/((q)/(2)[2a_(1)+(q-1)d])=(p^(2))/(q^(2))`
`implies (2a_(1)+(p-1)d)/(2a_(1)+(q-1)d)=(p)/(q)implies (a_(1)+((p-1)/(2))d)/(a_(1)+((q-1)/(2))d)=(p)/(q)`
For `(a_(6))/(a_(21)),p=11" and " q=41 implies(a_(6))/(a_(21))=(11)/(41)`.
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