Find the sum of the first seven numbers which | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $9$.

Similar Questions

Prove that $(a-b)^{2}, (a^{2}+b^{2})$ and $(a+b)^{2}$ form an $A.P.$

The sum of the first $n$ terms of an $A.P.$ is given by $S_n = 3n^2 + 5n$. Then,the $n^{th}$ term of the $A.P.$ $T_n = \ldots$

Find the $n^{th}$ term of the $A.P. \, 18, 16.5, 15, 13.5, \ldots$

With respect to the usual notations of an $A.P.$,if $a=3, n=8$ and $S_{n}=192$,find the common difference $d$.

$A$ person saved $Rs. 16,500$ in all during $10$ years. After the first year,every year he saved $Rs. 100$ more than what he had saved the previous year. Find his savings of the first year.

Vedclass Test Series

Exam Paper Generator

Online Exam Module