Question 57943
 Bill was the first to arrive - consider him the first group. Each group that arrived after Bill had two more people than the group that arrived before it. How many people were in school after 20 groups arrived? 
#=1+3+5+7+...+(1+19(2))
This is an aritmetic sequence with 1st number being 1
and the difference between consecutive terms being 2
If you add 20 of these terms you get
Sum = 1+3+5+7+....+35+37+39
Now, if you write this backward you get
Sum= 39+37+35+33..+5+3+1
If you add these two lines term by term you will get:
2Sum= 40+40+40+.....+40+40+40  
And you will get this 20 times.
So twice the Sum = 20(40)
Sum = (1/2)*20*40=400
The general formula is Sum(n terms)=(1/2)*n(1st term + last term)
and is usually written S(n)=(n/2)(a+last)
Cheers,
Stan H.