Question

The sum of n consecutive integers is 11. If the least of these integers is -10 what is the value of n ?

Answer 1

Hint:

The sum of the first n terms of any arithmetic sequence is

Sn = (n*(2*a1 + d*(n-1)))/2

In this case, Sn = 11, a1 = -10 and d = 1, so plug this into the formula above to get

11 = (n*(2*(-10) + 1*(n-1)))/2

11*2 = n*(-20 + n-1)

-20n + n^2-n = 22

Keep going to solve for n.