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Q)

Find the sum of all natural numbers between 45 and 300 that are exactly divisible by 7.

$\begin{array}{1 1} 300 \\ 6174 \\ 245 \\ 36 \end{array}$

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A)
Answer : (b) 6174
Explanation : $1^{st}\;term\;greater\;than\;or\;equal\;to\;45\;that\;is\;divisible\;by\;7=>\;49$
$last\;term\;<\;300=>294.$
$a=49\;,d=7\;,t_{n}=294\;find\;\;n$
$t_{n}=294=49+7(n-1)$
$7(n-1)=245$
$n-1=35$
$n=36$
$Find\;sum\;S_{n}=\frac{n}{2}\;[2a+(n-1)d]$
$S_{n}=\frac{36}{2}\;[2*49+35*7]$
$=6174.$