Find the sum of multiples of 5 lying between | vedclass

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(A) The multiples of $5$ between $84$ and $719$ form an Arithmetic Progression $(AP)$.The first multiple of $5$ after $84$ is $a = 85$.The last multip

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$50,800$

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(A) The multiples of $5$ between $84$ and $719$ form an Arithmetic Progression $(AP)$.The first multiple of $5$ after $84$ is $a = 85$.The last multiple of $5$ before $719$ is $l = 715$.The common difference is $d = 5$.Using the formula for the $n^{th}$ term: $a_n = a + (n - 1)d$.$715 = 85 + (n - 1)5$.$630 = (n - 1)5$.$n - 1 = 126$.$n = 127$.The sum of an $AP$ is given by $S_n = \frac{n}{2}(a + l)$.$S_{127} = \frac{127}{2}(85 + 715)$.$S_{127} = \frac{127}{2}(800)$.$S_{127} = 127 	imes 400 = 50,800$.

Find the sum of multiples of $5$ lying between $84$ and $719$.

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