Question

What conjecture can you make about the sum of the frst 25 positive even numbers?Make a conjecture. Choose the correct answer below.O A. The sum is equal to the number of terms squared.OB. The sum is the product of the number of terms and the number of terms plus one.O C. The sum is the product of the number of terms and twoOD. The sum is the product of the number of terms and the number of terms minus one.

Answer 1

Given:

2+4+6+8+10+.....+50

`2+4+6+10+\cdots+50=2(1+2+3+\cdots+25)`

Let the sum of the first n natural numbers be

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

Therefore the sum of first 25 positive even numbers is

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

Therefore,The sum is the product of the number of terms and the number of terms plus one.

Option B is the correct answer.