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  4. If a, b, c are positive numbers in A.P., such that their product is 64, then the minimum value of b is equal to

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Q. If $a, b, c$ are positive numbers in $A.P$., such that their product is $64$, then the minimum value of $b$ is equal to

Sequences and Series

Solution:

Given $a+c = 2b $
Also $\frac{a+b+c}{3} \ge \sqrt[3]{abc} $
$= \sqrt[3]{64} = 4 $
$ \Rightarrow \frac{3b}{3} \ge 4$
$ \Rightarrow b\ge 4$
$ \Rightarrow $ minimum value of $b = 4 $