Solve for the sum of all positive integers, from 5 to 1255, that can be divided by 5.

The sum of all the numbers which are multiple of 5 between 5 an 1255 is 158,130

Step-by-step explanation:

In this question, we are asked to calculate the sum of all positive numbers that can be divided by 5 between 5 and 1255

To calculate this, we make use of the sum of an arithmetic progression

Mathematically, we have this as

Sn = n/2[a + L]

Where n is the number of terms which we do not know yet

a is the first term which is 5 and L is the last term which is 1255

Now to get n, we make use of the formula for finding the nth term of an arithmetic sequence

Tn = a + (n-1) d

where a is the first term which is 5 and d is the common difference which is also 5 with our Tn which is 1255

Substituting these values into the last term equation, we have

1255 = 5 + (n-1) 5

1255 = 5 + 5n - 5

5n = 1255

n = 1255/5

n = 251

This means the number of terms we have in this arithmetic series is 251

Now we plug this n value into the sum equation

Thus,

Sn = 251/2 (5 + 1255)

Sn = 251/2 (1260)

Sn = 251 * 630

Sn = 158,130