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(D) The first $30$ positive multiples of $6$ form an Arithmetic Progression $(A.P.)$ where the first term $a = 6$ and the common difference $d = 6$.Th

Vedclass · Accepted Answer

$2790$

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(D) The first $30$ positive multiples of $6$ form an Arithmetic Progression $(A.P.)$ where the first term $a = 6$ and the common difference $d = 6$.The $30^{th}$ term (last term) is $l = 6 	imes 30 = 180$.The sum of $n$ terms of an $A.P.$ is given by the formula $S_n = \frac{n}{2}(a + l)$.Substituting the values $n = 30$,$a = 6$,and $l = 180$:$S_{30} = \frac{30}{2}(6 + 180)$$S_{30} = 15 	imes 186$$S_{30} = 2790$.

The sum of the first $30$ positive multiples of $6$ is:

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