Use the formula to find the sum of the numbers 101-110.
S=x+(x+1)+(x+2)+...+(y-2)+(y-1)+y (the sum of n integers from x to y)

S=y+(y-1)+(y-2)+...+(x+2)+(x+1)+x (the same sum in reverse order)

2s=(x+y)+(x+y)+(x+y)+...+(x+y)+(x+y)+(x... Add the equations.

2s=n(x+y) There are n terms of (x+y).
S=n(x+y)/2 Divide each side by 2.

Question

Use the formula to find the sum of the numbers 101-110. 
S=x+(x+1)+(x+2)+...+(y-2)+(y-1)+y (the sum of n integers from x to y) 

S=y+(y-1)+(y-2)+...+(x+2)+(x+1)+x (the same sum in reverse order) 

2s=(x+y)+(x+y)+(x+y)+...+(x+y)+(x+y)+(x... Add the equations. 

2s=n(x+y) There are n terms of (x+y). 
S=n(x+y)/2 Divide each side by 2.

sshayer · Answer

numbers are 101,102,103,104,105,106,107,108,109,110
number of numbers n=10
$$s=\frac{ 10(101+110) }{ 2 }=?$$