QJEEM06Ma42aa: JEE Main 2006 Mathematics - Class 11 JEEM06Ma42aa Solution: Let , , .....be terms on A.P. If equals

Question

Verified Solution • 2025–26 Session moderate

Let

{a_1}

,

{a_2}

,

{a_3}

.....be terms on A.P. If

{{{a_1} + {a_2} + .....{a_p}} \over {{a_1} + {a_2} + .....{a_q}}} = {{{p^2}} \over {{q^2}}},\,p \ne q,\,then\,{{{a_6}} \over {{a_{21}}}}\,

equals

Accepted Answer

{{{p \over 2}\left[ {2{a_1} + \left( {p - 1} \right)d} \right]} \over {{q \over 2}\left[ {2{a_1} + \left( {q - 1} \right)d} \right]}} = {{{p^2}} \over {{q^2}}}

\Rightarrow {{2{a_1} + \left( {p - 1} \right)d} \over {2{a_1} + \left( {p - 1} \right)d}} = {p \over q}

{{{a_1} + \left( {{{p - 1} \over 2}} \right)d} \over {{a_1} + \left( {{{q - 1} \over 2}} \right)d}} = {p \over q}

For

{{{a_6}} \over {a{}_{21}}},\,\,p = 11,\,q = 41

\Rightarrow {{{a_6}} \over {a{}_{21}}} = {{11} \over {41}}

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