90
Find the sum of all $3$-digit natural numbers which are divisible by $11$.
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$3$ - digit natural numbers divisible by $11$ are
$110, 121, ..., 990$ ($1/2$)
Here first term $= 110$ and common difference $= 11$
$a_n = 990$
$\Rightarrow 110 + (n - 1) \times 11 = 990$ ($1$)
$\Rightarrow n = 81$ ($1/2$)
$S_{81} = \frac{81}{2} \times [110+990]$
$= 44550$ ($1$)
$110, 121, ..., 990$ ($1/2$)
Here first term $= 110$ and common difference $= 11$
$a_n = 990$
$\Rightarrow 110 + (n - 1) \times 11 = 990$ ($1$)
$\Rightarrow n = 81$ ($1/2$)
$S_{81} = \frac{81}{2} \times [110+990]$
$= 44550$ ($1$)