QJEEM22Ma0d3d: JEE Main 2022 Mathematics - Class 11 JEEM22Ma0d3d Solution: If a 1 (> 0), a 2 , a 3 , a 4 , a 5 are in a G.P., a 2 + a 4 =…

Let G.P. be a₁ = a, a₂ = ar, a₃ = ar², .........

$\because$ 3a₂ + a₃ = 2a₄

$\Rightarrow$ 3ar + ar² = 2ar³

$\Rightarrow$ 2ar² $-$ r $-$ 3 = 0

$\therefore$ r = $-$ 1 or ${3 \over 2}$

$\because$ a₁ = a > 0 then r $\ne$ $-$ 1

Now, a₂ + a₄ = 2a₃ + 1

ar + ar³ = 2ar² + 1

$a\left( {{3 \over 2} + {{27} \over 8} - {9 \over 2}} \right) = 1$

$\therefore$ a = ${8 \over 3}$

$\therefore$ a₂ + a₄ + 2a₅ = a(r + r³ + 2r⁴)

$= {8 \over 3}\left( {{3 \over 2} + {{27} \over 8} + {{81} \over 8}} \right) = 40$