QJEEM24Mac352: JEE Main 2024 Mathematics - Class 11 JEEM24Mac352 Solution: If , then the value of is ____________.

Question

Verified Solution • 2025–26 Session moderate

If

8=3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2 p)+\frac{1}{4^3}(3+3 p)+\cdots \cdots \infty

, then the value of

p

is ____________.

Accepted Answer

$8 = \frac{3}{1 - \frac{1}{4}} + \frac{p \cdot \frac{1}{4}}{{(1 - \frac{1}{4})}^{2}}$

$(sum of infinite terms of A.G.P = \frac{a}{1 - r} + \frac{d r}{(1 - r)^{2}})$

$\Rightarrow \frac{4 p}{9} = 4 \Rightarrow p = 9$

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