If in A.P. is such that a_4 a_7 =2 3 , find a_6 a_8 . - Vidyadip

Question

If in A.P. is such that $\frac{\text{a}_4}{\text{a}_7}=\frac{2}{3},$ find $\frac{\text{a}_6}{\text{a}_8}.$

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Answer

$\frac{\text{a}_4}{\text{a}_7}=\frac{2}{3}$ [Given]
$\Rightarrow\frac{\text{a}+3\text{d}}{\text{a}+6\text{d}}=\frac{2}{3}$
$\Rightarrow3\text{a}+9\text{d}=2\text{a}+12\text{d}$
$\Rightarrow\text{a}=3\text{d}\ .....(1)$
$\frac{\text{a}_6}{\text{a}_8}=\frac{\text{a}+5\text{d}}{\text{a}+7\text{d}}$ $[\because3\text{d from}(1)]$
$\Rightarrow\frac{8\text{d}}{10\text{d}}$
$\Rightarrow\frac{4}{5}$
$\frac{\text{a}_6}{\text{a}_8}=\frac{4}{5}$

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