Question

Find the sum of all numbers between 50 and 350 that are divisible by 6

Answer 1

(sum of numbers divisible by 6 from 1 to 350) - (
sum of numbers divisible by 6 from 1 to 50)

10266-216
=10050

Answer 2

Answer:

The sum of all numbers between 50 and 350 that are divisible by 6 is 10050.

Step-by-step explanation:

All the numbers between 50 and 350 that are divisible by 6 are

54, 60,...,348

It is an AP, where first term is 54 and common difference is 6.

nth term of an AP is

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

$348=54+(n-1)6$

$294=(n-1)6$

$49=n-1$

$50=n$

The number of term between 50 and 350 that are divisible by 6 is 50.

The sum of n terms of an AP is

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

$S_{50}=\frac{50}{2}[2(54)+(50-1)(6)]=10050$

Therefore the sum of all numbers between 50 and 350 that are divisible by 6 is 10050.