What is the sum of the multiples of 4 from 16 to 100?

Solution:

Multiples are numbers that we get when we multiply one whole number by another whole number

The multiples of 4 is given by 4 × n. Thus, the multiples of 4 from 16 to 100 = 16, 20, 24, ........., 100.

Here,

a₁ = 16, a_n = 100, d = 4

By arithmetic sequence formula,

a_n = a₁ + (n - 1)d 

100 = 16 + (n - 1)4

100 = 16 + 4n - 4

4n = 100 - 12

n = 88/4 = 22

By sum of arithmetic sequence formula,

Now, sum S_n = n(a₁ + a_n) / 2

= 22(16 + 100) / 2

= (22 × 116)/2 = 2552/2 = 1276.

Thus, the sum would be: 16 + 20 + ... + 100 = 1276.

Thus, the sum of the multiples of 4 from 16 to 100 is 1276.

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What is the sum of the multiples of 4 from 16 to 100?

Summary:

The sum of the multiples of 4 from 16 to 100 is 1276.