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Q.
If $x \in R$, the numbers $\left(5^{1+x}+5^{1-x}\right), a / 2,\left(25^x+25^{-x}\right)$ form an A.P. then ' $a$ ' must lie in the interval
Sequences and Series
Solution:
$5^{1+ x }+5^{1- x }, a / 2,25^{ x }+25^{- x }$
$2\left(\frac{ a }{2}\right)=5\left(5^{ x }+\frac{1}{5^{ x }}\right)+\left(25^{ x }+\frac{1}{25^{ x }}\right) $
$a_{\min }=5(2)+2=12 $
$a_{\max }=\infty \Rightarrow [12, \infty)$