When you sum consecutive numbers, if there are an odd number of consecutive numbers then the answer is the middle number times the total amount of numbers. As shown in this formula
if a,b,c,d,e,f,g,h,i,j,k are consecutive numbers then
a+b+c+d+e+f+g+h+i+j+k=11f
The formula can be proved using substitution.
If a=1, b=2, c=3, d=4, e=5, f=6, g=7, h=8, i=9, j=10, k=11
1+2+3+4+5+6+7+8+9+10+11=11x6
66=11x6
66=66
It canalso be shown with this formula
final answer=x
middle number=y
y+1+y+2+y+3+y+4+y+5+y-1+y-2+y-3+y-4+y-5=x
11y+1+2+3+4+5-1-2-3-4-5=x
11y=x
This formula can also be proved with substitution
x=66
y=6
6+1+6+2+6+3+6+4+6+5+6-1+6-2+6-3+6-4+6-5=x
11*6+1+2+3+4+5-1-2-3-4-5=x
11*6=x
66=x