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Find the Sum of All Integers Between 84 and 719, Which Are Multiples of 5. - Mathematics

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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.4 | Q 8 | Page 30
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