Mathematics · Sequence and Series

JEE Main 2024 — 1 February, Shift 1 — Question 17

Let $3, a, b, c$ be in A.P. and $3, a-1, b+1, c+9$ be in G.P. Then, the arithmetic mean of $a, b$ and $c$ is :

Answer: D

$3, \mathrm{a}, \mathrm{b}, \mathrm{c} \rightarrow$ A.P

$\quad \Rightarrow 3,3+\mathrm{d}, 3+2 \mathrm{~d}, 3+3 \mathrm{~d}$

$3, \mathrm{a}-1, \mathrm{~b}+1, \mathrm{c}+9 \rightarrow$ G.P

$\Rightarrow 3,2+\mathrm{d},4+2\mathrm{~d},12+3\mathrm{~d}$

$\mathrm{a}=3+\mathrm{d} \quad(2+d)^{2}=3(4+2 d)$

$b=3+2 d$

$\mathrm{d}=4,-2$

$\mathrm{c}=3+3 \mathrm{~d}$

If $\mathrm{d}=4 \quad$ G.P

$\Rightarrow 3,6,12,24$

$\mathrm{a}=7$

$b=11$

$\mathrm{c}=15$

$\frac{a+b+c}{3}=11$

Answer key and solution verified before publishing.

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