JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_1, a_2, a_3, \ldots\) be in an arithmetic progression of positive terms. Let \(\mathrm{A}_{\mathrm{k}}=\mathrm{a}_1{ }^2-\mathrm{a}_2{ }^2+\mathrm{a}_3{ }^2-\mathrm{a}_4{ }^2+\ldots+\mathrm{a}_{2 \mathrm{k}-1}{ }^2-\mathrm{a}_{2 \mathrm{k}}{ }^2\). If \(\mathrm{A}_3=-153, \mathrm{~A}_5=-435\) and \(\mathrm{a}_1{ }^2+\mathrm{a}_2{ }^2+\mathrm{a}_3{ }^2=66\), then \(\mathrm{a}_{17}-\mathrm{A}_7\) is equal to ....................
- A \(920\)
- B \(852\)
- C \(910\)
- D \(911\)
Answer & Solution
Correct Answer
(C) \(910\)
Step-by-step Solution
Detailed explanation
\( \mathrm{d} \rightarrow \text { common diff. } \) \( \mathrm{A}_{\mathrm{k}}=-\mathrm{kd}[2 \mathrm{a}+(2 \mathrm{k}-1) \mathrm{d}] \) \( \mathrm{A}_3=-153 \) \( \Rightarrow 153=13 \mathrm{~d}[2 \mathrm{a}+5 \mathrm{~d}] \) \( 51=\mathrm{d}[2 \mathrm{a}+5 \mathrm{~d}] \)…
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