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ધારો કે $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \ldots$ એ ધન પદોવાળી સમાંતર શ્રેણી છે. ધારોકે
$A_k=a_1^2-a_2^2+a_3^2-a_4^2+\ldots+a_{2 k-1}^2-a_{2 k}^2$ .
જો $\mathrm{A}_3=-153, \mathrm{~A}_5=-435$ અને $\mathrm{a}_1^2+\mathrm{a}_2^2+\mathrm{a}_3^2=66$ હોય, તો $\mathrm{a}_{17}-\mathrm{A}_7=$............
$920$
$852$
$910$
$911$
Solution
$ \mathrm{d} \rightarrow \text { common diff. } $
$ \mathrm{A}_{\mathrm{k}}=-\mathrm{kd}[2 \mathrm{a}+(2 \mathrm{k}-1) \mathrm{d}] $
$ \mathrm{A}_3=-153 $
$ \Rightarrow 153=13 \mathrm{~d}[2 \mathrm{a}+5 \mathrm{~d}] $
$ 51=\mathrm{d}[2 \mathrm{a}+5 \mathrm{~d}] $
$ \mathrm{A}_5=-435 $
$ 435=5 \mathrm{~d}[2 \mathrm{a}+9 \mathrm{~d}] $
$ 87=\mathrm{d}[2 \mathrm{a}+9 \mathrm{~d}] $
$ (2)-(1) $
$ 36=4 \mathrm{~d}^2$
$ \mathrm{~d}=3, \mathrm{a}=1 $
$ \mathrm{a}_{17}-\mathrm{A}_7=49-[-7.3[2+39]]=910$
