Let l_1, l_2, ldots, l_{100} be consecutive t | vedclass

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Question

Given

$A _{51}- A _{50}=1000 \Rightarrow \ell_{S 1} w _{ S1 }-\ell_{50} w _{S 0}=1000$

$\Rightarrow\left(\ell_1+50 d _1\right)\left( w _1+50 d _

Vedclass · Accepted Answer

$18900$

Vedclass · Answer

Given

$A _{51}- A _{50}=1000 \Rightarrow \ell_{S 1} w _{ S1 }-\ell_{50} w _{S 0}=1000$

$\Rightarrow\left(\ell_1+50 d _1ight)\left( w _1+50 d _2ight)-\left(\ell_1+49 d _1ight)\left( w _1+49 d _2ight)=1000$

$\Rightarrow\left(\ell_1 d _2+ w _1 d _1ight)=10$

(As $d _1 d _2=10$ )

$	herefore A _{100}- A _{90}=\ell_{100} w _{100}-\ell_{90} w _{90}$

$=\left(\ell_1+99 d _1ight)\left( w _1+99 d _2ight)-\left(\ell_1+89 d _1ight)\left( w _1+89 d _2ight)$

$=10\left(\ell_1 d _2+ w _1 d _1ight)+\left(99^2-89^2ight) d _1 d _2$

$=10(10)+\frac{(99-89)}{-10}(99+89)(10)$

$\left(	ext { As, } d_1 d_2=10ight)$

$=100(1+188)=100(189)$

$=18900$

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