danielacampos364
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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.

Look at the table Make a conjecture about the sum of the first 25 positive even numbers AThe sum is 25 26 BThe sum is 24 25 CThe sum is 24 24 DThe sum is 25 25 class=

Respuesta :

carlosego

Answer:

A) The sum is 25 × 26

Step-by-step explanation:

In the attached table we notice a pattern.

For the first positive pair number the sum is [tex]S = (1)(2)[/tex]

For the first two positive pairs, the sum is [tex]S = (2)(3)[/tex]

For the first three positive pairs, the sum is [tex]S = (3)(4)[/tex].

So:

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

[tex]S = n(n + 1)[/tex]

If [tex]n = 25[/tex], and [tex]n+1 = 26[/tex] then, the sum of the first 25 positive even numbers is:

[tex]S = (25)(26) = 650[/tex]

The correct answer is option A

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