If three positive numbers a, b and c are in A.P. such that abc, = 8 , then minimum possible value of

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8. Sequences and Series

hard

If three positive numbers $a, b$ and $c$ are in $A.P.$ such that $abc\, = 8$, then the minimum possible value of $b$ is

$2$

$4^{\frac{1}{3}}$

$4^{\frac{2}{3}}$

$4$

(JEE MAIN-2017)

Solution

By Arithmetic Mean: $a + c\, = 2b$
Consider $a\, = b\, = c\, = 2$
$ \Rightarrow $ $abc\, = 8$
$ \Rightarrow $ $a + b\, = 2b$
minimum possible value of $b\, = 2$

Standard 11

Mathematics

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medium

(JEE MAIN-2020)

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easy

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medium

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If $\frac{{3 + 5 + 7 + ……….{\rm{to}}\;n\;{\rm{terms}}}}{{5 + 8 + 11 + ………{\rm{to}}\;10\;{\rm{terms}}}} = 7$, then the value of $n$ is

easy

If three positive numbers $a, b$ and $c$ are in $A.P.$ such that $abc\, = 8$, then the minimum possible value of $b$ is

Solution

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