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 [tex]I^+[/tex] = 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
[tex]a_n = a+ (n-1) d\\\implies 395 = 5 + (n-1) 5\\\implies 78 = n - 1 \implies n = 79[/tex]
⇒There are total 79 terms in the series.
So, SUM OF 79 TERMS =
[tex]S_n = \frac{n}{2} (a + a_n) \\\implis S_{79} = \frac{79}{2} (5 + 395) = 15,800\\\implies S_{79} = 15,800[/tex]
Hence, The sum of all positive integers less than 400 which are divisible by 5 is 15,800.
