If a _{1}, a _{2}, a _{3} ldots and b _{1}, b | vedclass

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Question

$a_{1}, a_{2}, a_{3} \ldots 	ext { A.P. } ; a_{1}=2 ; a_{10}=3 ; d_{1}=\frac{1}{9}$

$b _{1}, b _{2}, b _{3}, \ldots$ $A.P.$ $; b _{1}=\frac{1}{2}

Vedclass · Accepted Answer

$\frac{28}{27}$

Vedclass · Answer

$a_{1}, a_{2}, a_{3} \ldots 	ext { A.P. } ; a_{1}=2 ; a_{10}=3 ; d_{1}=\frac{1}{9}$

$b _{1}, b _{2}, b _{3}, \ldots$ $A.P.$ $; b _{1}=\frac{1}{2} ; b _{10}=\frac{1}{3} ; d _{2}=\frac{-1}{54}$

[Using $a_{1} b_{1}=1=a_{10} b_{10} ; d_{1}$ and $d_{2}$ are common differences respectively]

$a _{4} \cdot b _{4} =\left(2+3 d _{1}ight)\left(\frac{1}{2}+3 d _{2}ight)$

$=\left(2+\frac{1}{3}ight)\left(\frac{1}{2}-\frac{1}{18}ight)$

$=\left(\frac{7}{3}ight)\left(\frac{8}{18}ight)=\frac{28}{27}$

If $a _{1}, a _{2}, a _{3} \ldots$ and $b _{1}, b _{2}, b _{3} \ldots$ are $A.P.$ and $a_{1}=2, a_{10}=3, a_{1} b_{1}=1=a_{10} b_{10}$ then $a_{4} b_{4}$ is equal to

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