The sum of integers from 1 to 50 that are divisible by 2 and 3 is
The sum of integers from 1 to 50 that are divisible by 2 and 3 is
316
$6^3$
36
48
Solution
Let sum of integers from 1 to 50 that are divisible by 2 and 3 (i.e. 6 ) is $S$ $\therefore S=6+12+18+\ldots+48 \ldots$ (i) $\{\because$ Smallest integer and largest integer divisible by 6 and between 1 and 50 are 6 and 48 respectively \} $6,12,18, \ldots, 48$ (this is an AP)
$
\begin{aligned}
& & a & =6, a_n=48 \text { and } d=6 \\
\because & & a_n & =a+(n-1) d \\
\Rightarrow & & 48 & =6+(n-1) 6 \Rightarrow 42=(n-1) 6 \\
\Rightarrow & & 7 & =n-1 \Rightarrow n=8 \\
\therefore & & S & =\frac{n}{2}\left[a+a_n\right]=\frac{8}{2}(6+48) \\
& & & =4(54)=216=6^3
\end{aligned}
$