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?

Answer 1

n(n +1) is the Total number of seats in the corner section.

Explanation:

We are given that:

Number of seats in first row = 2

Number of seats in second row = 4

Number of seats in third row = 6

:

Number of seats in
`n^(th)` row =
`2n`

We can clearly see that it is an Arithmetic progression with

First term, a = 2

Common Difference, d = 2

`n^(th)` term,
`a_n=2n`

To find: Total number of seats in corner sections with n rows.

i.e. Sum of n terms of above AP.

Formula for sum of n terms of an AP:

`S_n=(n)/(2)(2a+(n-1)d)\\`

Putting the values:

`\Rightarrow (n)/(2) ({2 * 2 +(n-1)2})\\\Rightarrow (n)/(2) (4 +2n-2)\\\Rightarrow (n)/(2) (2n +2)\\\Rightarrow (n)/(2) * 2(n +1)\\\Rightarrow n(n +1)`

n(n +1) is the Total number of seats in the corner section.