QJEEAdv17Ma2ca5: JEE Advanced 2017 Mathematics - Class 11 JEEAdv17Ma2ca5 Solution: If a 4 = 28, then p + 2q =

Question

Verified Solution • 2025–26 Session moderate

If a₄ = 28, then p + 2q =

Accepted Answer

α = \frac{1 + \sqrt{5}}{2}

,

β = \frac{1 - \sqrt{5}}{2}

a_{4} = a_{3} + a_{2}

= 2 a_{2} + a_{1}

= 3 a_{1} + 2 a_{0}

28 = p (3 α + 2) + q (3 β + 2)

28 = (p + q) (\frac{3}{2} + 2) + (p - q) (\frac{3 \sqrt{5}}{2})

∴

p

-

q = 0

and

(p + q) \times \frac{7}{2} = 28

\Rightarrow

p + q = 8

\Rightarrow

p = q = 4

∴

p + 2q = 12

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