What conjecture can you make about the sum of the first 22 positive even numbers?

A.) The sum of the product of the number of terms and the number of terms plus one.

B.) The sum is the product of the number of terms and the number of terms minus one.

C.) The sum is the product of the number of terms and two.

D.) The sum is equal to the number of terms squared.

Question

Carissa Mendoza

Mathematics

4 November, 13:22

What conjecture can you make about the sum of the first 22 positive even numbers?

A.) The sum of the product of the number of terms and the number of terms plus one.

B.) The sum is the product of the number of terms and the number of terms minus one.

C.) The sum is the product of the number of terms and two.

D.) The sum is equal to the number of terms squared.

+5

Answers (1)

Know the Answer?

Geovanni Rowe · Answer 1

A.) The sum of the product of the number of terms and the number of terms plus one.

Step-by-step explanation:

So, we have the sum of the first 22 positive even numbers:

S = 2 + 4 + 6 + ... + 44

We know the sum of such sequence is given by the (sum of the first number (2) and the last number (44)) multiplied by the number of terms (11).

S = (2 + 44) * 11 = 46 * 11 = 506

Answer A tells us it should be the sum of the number of terms (22) by the number of terms plus one (22 + 1 = 23).

S = 22 * 23 = 506

That's confirmed.

Answer B would give 22 * 21 = 462, so it's not right

Answer C would give 22 * 2 = 44, obviously not right

Answer D would give 22 * 22 = 484, close but not right.