Question

The sum of all positive integers less than 400 which are divisible by 5. Can someone give me the steps to do this?

Answer 1

Sum of all positive integers less than 400 and divisible by 5 is 15,800.

Explanation:

TO FIND :

The sum of all positive integers less than 400 which are divisible by 5.

The set of positive integers
`I^+` = 1,2,3, 4,5,6,7,.........,,

Now, the number should be divisible by 5.

SO, the desired set of positive integers = { 5,10,15,20,.......}

Again the numbers are LESS than 400.

So, the desired set of positive integers = { 5,10,15,20,....... 385,390, 395}

Here, First term a = 5, common difference d = 4 and last term an = 395

`a_n = a+ (n-1) d\\\implies 395 = 5 + (n-1) 5\\\implies 78 = n - 1 \implies n =  79`

⇒There are total 79 terms in the series.

So, SUM OF 79 TERMS =

`S_n = (n)/(2) (a + a_n) \\\implis S_(79) = (79)/(2) (5 + 395)  = 15,800\\\implies S_(79) = 15,800`

Hence, The sum of all positive integers less than 400 which are divisible by 5 is 15,800.