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Find the sum of all integers between 100 and 550, which are divisible by 9.
Given:
To do:
We have to find the sum of all
Solution:
Integers between 100 and 550, which are divisible by 9 are \( 108,117,126, \ldots, 549 \).
The sequence is in A.P.
Here,
\( a=108 \) and \( d=117-108=9 \) \( l=549 \)
We know that,
$l=a+(n-1) d$
$\Rightarrow 549=108+(n-1) \times 9$
$\Rightarrow 549=108+9n-9$
$\Rightarrow 549-99=9 n$
$\Rightarrow n=\frac{450}{9}=50$
$\therefore n=50$
$\mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d]$
$=\frac{50}{2}[2 \times 108+(50-1) \times 9]$
$=25[216+49 \times 9]$
$=25(216+441)$
$=25 \times 657$
$=16425$
The sum of all integers between 100 and 550 which are divisible by 9 is $16425$.
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