JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_1, a_2, a_3, \ldots\) be an A.P. and \(g_1 = a_1, g_2, g_3, \ldots\) be an increasing G.P. If \(a_1 = a_2 + g_2 = 1\) and \(a_3 + g_3 = 4\), then \(a_{10} + g_5\) is equal to:
- A \(81\)
- B \(76\)
- C \(62\)
- D \(55\)
Answer & Solution
Correct Answer
(D) \(55\)
Step-by-step Solution
Detailed explanation
Let the common difference of the A.P. be \(d\) and the common ratio of the G.P. be \(r\). Given \(a_1 = 1\) and \(g_1 = a_1 = 1\). From \(a_2 + g_2 = 1\), we have: \((a_1 + d) + g_1 r = 1\) \(1 + d + r = 1 \Rightarrow d = -r\) From \(a_3 + g_3 = 4\), we have:…
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