Givens
The numbers are n and n + 1
Average = Av = 105
Equation
Av = (n)(n + 1)/2
Solution
Av = 105
n(n +1)/2 = 105 Multiply both sides by 2
n(n + 1) = 105 * 2
n(n + 1) = 210 Remove the brackets.
n^2 + n = 210 Subtract 210 from both sides
n^2 + n - 210 = 0
factor
(n+15)(n - 14)
n + 15 = 0
n = - 15
n = - 15 which is the smallest of the two answers.
n + 1 = - 14
