math  integers
posted by nicole on .
The sum of 25 consecutive integers is 1000. What is the smallest integer used as an addendum?

let the first term be a
clearly d = 1
sum(n) = (n/2)(2a + (n1)d)
1000 = (25/2)(2a + 24(1))
2000 = 25(2a + 24)
2000= 50a + 600
50a = 1400
a = 1400/50 = 28
check:
sum(25) = (25/2)( 56 + 24)
= 12.5(80) = 1000