Question

Look at the table. Make a conjecture about the sum of the first 25 positive even numbers.

A)The sum is 25 × 26. B)The sum is 24 × 25. C)The sum is 24 × 24. D)The sum is 25 × 25.

Answer 1

A) The sum is 25 × 26

Explanation:

In the attached table we notice a pattern.

For the first positive pair number the sum is
`S = (1)(2)`

For the first two positive pairs, the sum is
`S = (2)(3)`

For the first three positive pairs, the sum is
`S = (3)(4)`.

So:

For the first number of positive pairs, the sum of them is:

`S = n(n + 1)`

If
`n = 25`, and
`n+1 = 26` then, the sum of the first 25 positive even numbers is:

`S = (25)(26) = 650`

The correct answer is option A