Class 11

Math

Algebra

Sequences and Series

The minimum value of the sum of real numbers $a_{−5}+a_{−4}+3a_{−3},1,a_{8}$ and $a_{10}$ with $a>0$ is

Using $A.M≥G.M$

$⇒8a_{−5}+a_{−4}+a_{−3}+a_{−3}+a_{−3}+a_{8}+a_{10}+1 ≥1$

$⇒a_{−5}+a_{−4}+a_{−3}+a_{−3}+a_{−3}+a_{8}+a_{10}+1≥8$

$⇒(a_{−5}+a_{−4}+a_{−3}+a_{−3}+a_{−3}+a_{8}+a_{10}+1)_{min}=8$