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Question
Find the sum of all integers between 100 and 550, which are divisible by 9.
Solution
The integers between 100 and 550 that are divisible by 9 are:
108, 117...549
Here, we have:
\[a = 108\]
\[ d = 9\]
\[ a_n = 549\]
\[ \Rightarrow 108 + (n - 1)(9) = 549\]
\[ \Rightarrow 9n - 9 = 441\]
\[ \Rightarrow 9n = 450\]
\[ \Rightarrow n = 50\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ \Rightarrow S_{50} = \frac{50}{2}\left[ 2 \times 108 + (50 - 1) \times 9 \right]\]
\[ \Rightarrow S_{50} = 25\left( 657 \right)=16425\]
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