Find the sum of the multiples of 3 or 7 under 875 For example

Question

Find the sum of the multiples of 3 or 7 under 875
For example, if we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Answer 1

Multiples of 3 are an arithmetic sequence, a₁ = 3, d = 3.

To determine the number of terms

875 > 3 + (n - 1)3

872 > 3n - 3

875 > 3n

291 2/3 > n

There are 291 multiples of 3 less than 875.

a₂₉₁ = 873

S₂₉₁ = (291/2)[(2(3) + (291 - 1)3]

S₂₉₁ = (291/2)[6 + 870]

S₂₉₁ = (291/2)(876)

S₂₉₁ = (291)(438)

S₂₉₁ = 127458

 

The sum of the multiples of three less than 875 is 127,458.

 

Follow this model of calculate the sum of the multiples of seven less than 875 and add to the above.