JEE Main 2022 — Sequences And Series Question with Solution
From: JEE Main 2022 (Online) 26th June Evening Shift
Question
If a1 (> 0), a2, a3, a4, a5 are in a G.P., a2 + a4 = 2a3 + 1 and 3a2 + a3 = 2a4, then a2 + a4 + 2a5 is equal to ___________.
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Show full solutionCorrect answer: 40
Step-by-step explanation
Let G.P. be a1 = a, a2 = ar, a3 = ar2, .........
3a2 + a3 = 2a4
3ar + ar2 = 2ar3
2ar2 r 3 = 0
r = 1 or
a1 = a > 0 then r 1
Now, a2 + a4 = 2a3 + 1
ar + ar3 = 2ar2 + 1
a =
a2 + a4 + 2a5 = a(r + r3 + 2r4)
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