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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 $504$.