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JEE Main 202522 JanuaryMorning Shift

Exam: JEE Main
Year: 2025
Date: 22 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Sequences and Series

JEE Main 2025 · 22 January · Morning Shift · Mathematics · Sequences and Series

Let a_1, a_2, a_3, be a G.P. of increasing positive terms. If a_1...

Let

a_1, a_2, a_3, \ldots

be a G.P. of increasing positive terms. If

a_1 a_5=28

and

a_2+a_4=29

, then

a_6

is equal to:

Options

A $628$
B $812$
C $526$
D $784$

Correct answer

D. $784$

Step-by-step solution

\begin{aligned} & a_1 a_5=28 \Rightarrow a^2 r^4=28 \\ & a_2+a_4=29 \Rightarrow a r+a r^3=29 \end{aligned}

ar and

a r^3

are roots of

\begin{aligned} & k^2-29 k+28=0 \\ & \Rightarrow \quad k=1, k=28 \\ & a r=1, a r^3=28 \\ & r^2=28, a^2=\frac{1}{28} \\ & a_6=a r^5 \Rightarrow r^4=28^2 \\ & \Rightarrow a_6=784 \end{aligned}

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