Find the sum of all natural numbers lying bet | vedclass

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Question

The natural numbers lying between $100$ and $1000 ,$ which are multiples of $5,$ are $105,110,.......$ $995$

Here, $a=105$ and $d=5$

Here, $a=10

Vedclass · Accepted Answer

$98450$

Vedclass · Answer

The natural numbers lying between $100$ and $1000 ,$ which are multiples of $5,$ are $105,110,.......$ $995$

Here, $a=105$ and $d=5$

Here, $a=105$ and $d=5$

$a+(n-1) d=995$

$\Rightarrow 105+(n-1) 5=995$

$\Rightarrow(n-1) 5=995-105=890$

$\Rightarrow n-1=178$

$\Rightarrow n=179$

$	herefore S_{n}=\frac{179}{2}[2(105)+(179-1)(5)]$

$=\frac{179}{2}[2(105)+(178)(5)]$

$=179[105+(89) 5]$

$=179(105+445)$

$=(179)(550)$

$=98450$

Thus, the sum of all natural numbers lying between 100 and $1000,$ which are multiples of $5,$ $98450$

Find the sum of all natural numbers lying between $100$ and $1000,$ which are multiples of $5 .$

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