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(D) To find the sum of the first seven numbers that are multiples of both $2$ and $9$,we first find the least common multiple $(LCM)$ of $2$ and $9$.S

Vedclass · Accepted Answer

$504$

Vedclass · Answer

(D) To find the sum of the first seven numbers that are multiples of both $2$ and $9$,we first find the least common multiple $(LCM)$ of $2$ and $9$.Since $2$ and $9$ are coprime,their $LCM$ is $2 	imes 9 = 18$.The numbers that are multiples of both $2$ and $9$ are multiples of $18$,which form an arithmetic progression: $18, 36, 54, \ldots$Here,the first term $a = 18$ and the common difference $d = 18$.We need to find the sum of the first $n = 7$ terms using the formula $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values: $S_7 = \frac{7}{2}[2(18) + (7 - 1)18]$.$S_7 = \frac{7}{2}[36 + 6 	imes 18] = \frac{7}{2}[36 + 108] = \frac{7}{2}[144]$.$S_7 = 7 	imes 72 = 504$.

Find the sum of the first seven numbers which are multiples of $2$ as well as of $9$.

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