Question:
Find the sum of first seven numbers which are multiples of 2 as well as of 9.
Solution:
For finding, the sum of first seven numbers which are multiples of 2 as well as of 9. Take LCM of 2 and 9 which is 18.
So, the series becomes 18, 36, 54,…
Here, first term (a) = 18, common difference (of) = 36 -18 = 18
$\therefore \quad S_{7}=\frac{n}{2}[2 a+(n-1) d]=\frac{7}{2}[2(18)+(7-1) 18]$
$=\frac{7}{2}[36+6 \times 18]=7(18+3 \times 18)$
$=7(18+54)=7 \times 72=504$