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Question
Find the sum of all integers between 50 and 500 which are divisible by 7.
Solution
The integers between 50 and 500 that are divisible by 7 are:
56, 63...497
Here, we have:
\[a = 56\]
\[d = 7 \]
\[ a_n = 497\]
\[ \Rightarrow 56 + (n - 1)7 = 497\]
\[ \Rightarrow 7n - 7 = 441\]
\[ \Rightarrow 7n = 448\]
\[ \Rightarrow n = 64\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ \Rightarrow S_{64} = \frac{64}{2}\left[ 2 \times 56 + (64 - 1)7 \right]\]
\[ \Rightarrow S_{64} = 32\left[ 2 \times 56 + 63 \times 7 \right]=17696\]
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