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Question
Find the sum of all integers between 84 and 719, which are multiples of 5.
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Solution
The integers between 84 and 719, which are multiples of 5 are:
85, 90...715
Here, we have:
\[a = 85\]
\[d = 5\]
\[ a_n = 715\]
\[ \Rightarrow 85 + (n - 1)5 = 715\]
\[ \Rightarrow 5n - 5 = 630\]
\[ \Rightarrow n = 127\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ \Rightarrow S_{127} = \frac{127}{2}\left[ 2 \times 85 + (127 - 1)5 \right]\]
\[ \Rightarrow S_{127} = \frac{127}{2}\left[ 800 \right] = 50800\]
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