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How many numbers lie between $10$ and $300$, which when divided by $4$ leave a remainder $3$ ? Also, find their sum.
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$11, 15, ..., 299$
Here $a = 11$ and $d=4$
Let $a_n = 299$
$\Rightarrow 11 + (n-1) \times 4 = 299$
$\Rightarrow n = 73$
$S_{73} = \frac{73}{2} \times (11 +299) = 11315$
Here $a = 11$ and $d=4$
Let $a_n = 299$
$\Rightarrow 11 + (n-1) \times 4 = 299$
$\Rightarrow n = 73$
$S_{73} = \frac{73}{2} \times (11 +299) = 11315$