Prove your math skills

[BruceZ]

[ QUOTE ]
A lecture hall has 40rows of seats. there are 10 seats in the the first row (a1=10) 12 seats in the 2nd row and so on, with two more seats in each row than in the previous row. How many seats are in the lecture hall?

Whats the equation and answer?

[/ QUOTE ]

Last row has 10 + 39*2 = 88 seats.

S = 10 + 12 + 14 + 16 + ... + 88
S = 88 + 86 + 84 + 82 + ... + 10

2S = 98 + 98 + 98 + 98 + ... + 98

2S = 98*40

S = 98*40/2 = 1960.


In general for n terms starting with x and incrementing by c:

S = x + (x+c) + (x+2c) + (x+3c) + ... + [x + (n-1)c]

S = [(n-1)c + 2x]*n/2.