Question

What is the sum of all numbers between 50 to 350 that are divisible by 4?

Answer 1

Sum of all numbers between `50` to `350` that are divisible by `4` is `15000`.

Explanation:

As we are seeking numbers between `50` and `350` that are by `4`, the number divisible by `4` just after `50` is `52` and just before `350`, it is `348`.

Therefore, it is apparent that first number is `52` and then they follow as `56,60,64,.............,348` and say `348` is `n^(th)` term.

These are in an arithmatic sequence with first term as `a_1=52`, common difference as `4` and hence `n^(th)` term is `a_1+(n-1)d` and as `a_1=52` and `d=4`

we have `a_n=a_1+(n-1)d=348` i.e. `52+(n-1)xx4=348`

i.e. `4(n-1)=348-52=296`

or `n-1=296/4=74`

and `n=75`

As sum `S_n` of such an arithmatic series is given by

`S_n=n/2[a_1+a_n]`

= `75/2(52+348)`

= `75/2xx400`

= `75xx200`

= `15000`