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9 August, 18:44

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

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  1. 9 August, 22:28
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    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
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