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8. Sequences and Series
hard
For $\mathrm{x} \geq 0$, the least value of $\mathrm{K}$, for which $4^{1+\mathrm{x}}+4^{1-\mathrm{x}}$, $\frac{\mathrm{K}}{2}, 16^{\mathrm{x}}+16^{-\mathrm{x}}$ are three consecutive terms of an $A.P.$ is equal to :
A
$10$
B
$4$
C
$8$
D
$16$
(JEE MAIN-2024)
Solution
$ \mathrm{k}=4\left(4^{\mathrm{x}}+\frac{1}{4^{\mathrm{x}}}\right)+\left(4^{2 \mathrm{x}}+\frac{1}{4^{2 \mathrm{x}}}\right) $
$ \quad \geq 2 \quad \geq 2 $
$ \mathrm{k} \geq 10$
Standard 11
Mathematics
