Question

If 1 + 2 + 3 + 4 + .... + 50 = 25 k, then k = ______.

Options

• 50

• 51

• 49

• 26

Answer 1

If 1 + 2 + 3 + 4 + .... + 50 = 25 k, then k = 51.

Explanation:

The sum of the first n natural numbers is given by the formula:

`S_n= (n(n + 1))/2`

For n = 50, the sum is:

`S_50 = (50(50 + 1))/2`

= `(50 xx 51)/2`

= 25 × 51

= 1275

We are given that the sum equals 25 k:

1275 = 25 k

Divide both sides by 25:

k = `1275/25`

k = 51