Make a conjecture about the sum of the first 15 positive even number

I conclude that the sum will be even because any even number can be represented by 2n where n is a whole number

and even numbers are 2 apart, so

the sum of the first 15 are

2n+2 (n+1) + 2 (n+2) etc until we get to 2 (n+14)

we can undistribute the 2 from all of them and get

2 (n+n+1+n+2 ... n+14)

and we are sure that whatever is in the parenthasees is a whole number because whole+whole=whole

therefor, the sum is even

if you did want to find the sum then

an=2n

the 15th even number is 30

the first is 2

S15=15 (2+30) / 2=15 (32) / 2=15 (16) = 240

which is even