11, 13 and 15
note that consecutive odd integers have a difference of 2 between them
example : 1, 3 , 5
let the 3 consecutive integers be n , n+ 2, n + 4
The sum of the 3 integers divided by 3 gives the average, thus
[tex]\frac{n + n + 2 + n + 4}{3}[/tex] = 13
[tex]\frac{3n + 6}{3}[/tex]= 13 (multiply both sides by 3 to eliminate fraction )
3n + 6 = 3 × 13 = 39 ( subtract 6 from both sides )
3n = 39 - 6 = 33 ( divide both sides by 3 )
n = [tex]\frac{33}{3}[/tex] = 11
the integers are 11, 11 + 2, 11 + 4 = 11, 13, 15
