Find the sum of all positive multiples of 3 l | vedclass

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(C) The positive multiples of $3$ less than $50$ are $3, 6, 9, \dots, 48$.This is an arithmetic progression where the first term $a = 3$,the common di

Vedclass · Accepted Answer

$408$

Vedclass · Answer

(C) The positive multiples of $3$ less than $50$ are $3, 6, 9, \dots, 48$.This is an arithmetic progression where the first term $a = 3$,the common difference $d = 3$,and the last term $l = 48$.To find the number of terms $n$,we use the formula $l = a + (n - 1)d$:$48 = 3 + (n - 1)3$$45 = (n - 1)3$$15 = n - 1$$n = 16$.The sum $S_n$ of an arithmetic progression is given by $S_n = \frac{n}{2}(a + l)$:$S_{16} = \frac{16}{2}(3 + 48)$$S_{16} = 8 	imes 51 = 408$.

Find the sum of all positive multiples of $3$ less than $50$.

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