The sum of 25 consecutive integers is 1000. What is the smallest integer used as an addend.

Answer 1

the sum of the first n integers is

n(n+1)/2

Now, we have 25 integers starting somewhere else. That is, if the first one is k+1, then we add k to each value, giving us

nk + n(n+1)/2

So, using n=25,

25k + 25*26/2 = 1000
k + 13 = 40
k = 27

The numbers are 28,...,52

Checking our work, recall that the sum of n terms of an arithmetic sequence is

n(Ao+An)/2
= 25(28+52)/2 = 25*80/2 = 1000

Answer 2

Holy crap you know math