Answer:
Sum of all positive integers less than 400 and divisible by 5 is 15,800.
Step-by-step explanation:
TO FIND :
The sum of all positive integers less than 400 which are divisible by 5.
The set of positive integers
= 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](https://tex.z-dn.net/?f=a_n%20%3D%20a%2B%20%28n-1%29%20d%5C%5C%5Cimplies%20395%20%3D%205%20%2B%20%28n-1%29%205%5C%5C%5Cimplies%2078%20%3D%20n%20-%201%20%5Cimplies%20n%20%3D%20%2079)
⇒There are total 79 terms in the series.
So, SUM OF 79 TERMS =
![S_n = \frac{n}{2} (a + a_n) \\\implis S_{79} = \frac{79}{2} (5 + 395) = 15,800\\\implies S_{79} = 15,800](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%20%28a%20%2B%20a_n%29%20%5C%5C%5Cimplis%20S_%7B79%7D%20%3D%20%5Cfrac%7B79%7D%7B2%7D%20%285%20%2B%20395%29%20%20%3D%2015%2C800%5C%5C%5Cimplies%20S_%7B79%7D%20%3D%2015%2C800)
Hence, The sum of all positive integers less than 400 which are divisible by 5 is 15,800.