Find the average of first 25 multiples of 5. | vedclass

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Question

(A) The first $25$ multiples of $5$ are $5, 10, 15, \ldots, 125$.This forms an arithmetic progression where the first term $a = 5$,the last term $l =

Vedclass · Accepted Answer

$65$

Vedclass · Answer

(A) The first $25$ multiples of $5$ are $5, 10, 15, \ldots, 125$.This forms an arithmetic progression where the first term $a = 5$,the last term $l = 125$,and the number of terms $n = 25$.The sum of an arithmetic progression is given by $S_n = \frac{n}{2}(a + l)$.Sum $= \frac{25}{2}(5 + 125) = \frac{25}{2}(130) = 25 	imes 65 = 1625$.The average is given by $\frac{	ext{Sum}}{n} = \frac{1625}{25} = 65$.Alternatively,for an arithmetic progression,the average is $\frac{a + l}{2} = \frac{5 + 125}{2} = \frac{130}{2} = 65$.

Find the average of first $25$ multiples of $5$.

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