JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_{1}, a_{2}, \ldots, a_{10}\) be an \(AP\) with common difference \(-3\) and \(\mathrm{b}_{1}, \mathrm{~b}_{2}, \ldots, \mathrm{b}_{10}\) be a \(GP\) with common ratio \(2.\) Let \(c_{k}=a_{k}+b_{k}, k=1,2, \ldots, 10 .\) If \(c_{2}=12\) and \(\mathrm{c}_{3}=13\), then \(\sum_{\mathrm{k}=1}^{10} \mathrm{c}_{\mathrm{k}}\) is equal to ..... .
- A \(2021\)
- B \(1234\)
- C \(2227\)
- D \(2119\)
Answer & Solution
Correct Answer
(A) \(2021\)
Step-by-step Solution
Detailed explanation
\(c_{2}=a_{2}+b_{2}=a_{1}-3+2 b_{1}=12\) \(a_{1}+2 b_{1}=15....(1)\) \(c_{3}=a_{3}+b_{3}=a_{1}-6+4 b_{1}=13\) \(a_{1}+4 b_{1}=19....(2)\) from \((1)\, \,(2) b_{1}=2, a_{1}=11\)…
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