Find the sum of first seven numbers which are multiples of 2 as well as of 9 .
[Hint: Take the LCM of 2 and 9]

Given:

First seven numbers which are multiples of 2 as well as of 9.

To do:

We have to find the sum of first seven numbers which are multiples of 2 as well as of 9.

Solution:

Numbers that are multiples of 2 as well as 9 are the multiples of LCM of 2 and 9.

LCM of 2 and 9 $=2\times9=18$

 Numbers divisible by 18 are $18, 36,....., 90, 180,.....$

First seven numbers which are multiples of 2 and 9 are $18, 36, ......$

This series is in A.P.

Here,

First term $a=18$

Common difference $d=36-18=18$

Number of terms $n=7$

We know that,

$a_n=a+(n-1)d$

$a_7=18+(7-1)18$

$=18+6(18)$

We know that,

$\mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d]$

$=\frac{7}{2}[2 \times 18+(7-1) \times 18]$

$=\frac{7}{2}[36+6 \times 18]$

$=7(18+54)$

$=7\times 72$

$=504$

The sum of first seven numbers which are multiples of 2 as well as of 9 is $504$.      

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Updated on: 10-Oct-2022

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