The corner section of seats in a stadium contains 2 seats in the front row, 4 seats in the second row, 6 seats in the third row, etc. Each row has 2 more seats than the row in front of it. There are 2n seats in the nth row.

How many total seats are in a corner section with n rows of seats?
A)n2 + 2
B)n2 + n
C)n2 + 2n
D)n2 + 2n + 1

Question

The corner section of seats in a stadium contains 2 seats in the front row, 4 seats in the second row, 6 seats in the third row, etc. Each row has 2 more seats than the row in front of it. There are 2n seats in the nth row. 

How many total seats are in a corner section with n rows of seats?
A)n2 + 2
B)n2 + n
C)n2 + 2n
D)n2 + 2n + 1

anonymous · Answer

n^2 + n

anonymous · Answer

we have (2 + 4 + 6 + ... + 2n) = 2(1+2+3+...+n)

sum to n of natural numbers = (1/2)(n(n+1))

multiply by 2 to get B