The sum of integers from 1 to 50 that are divisible by 2 and 3 is

Step-by-step solution

Let sum of integers from 1 to 50 that are divisible by 2 and 3 (i.e. 6 ) is S S=6+12+18+ +48 (i) Smallest integer and largest integer divisible by 6 and between 1 and 50 are 6 and 48 respectively 6,12,18, , 48 (this is an AP) aligned & & a & =6, a_n=48 and d=6 & & a_n & =a+(n-1) d & & 48 & =6+(n-1) 6 42=(n-1) 6 & & 7 & =n-1 n=8 & & S & = n 2 [a+a_n ]= 8 2 (6+48) & & & =4(54)=216=6^3 aligned