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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?

Respuesta :

isyllus

Answer:

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

Step-by-step 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 [tex]n^{th}[/tex] row = [tex]2n[/tex]

We can clearly see that it is an Arithmetic progression with

First term, a = 2

Common Difference, d = 2

[tex]n^{th}[/tex] term, [tex]a_n=2n[/tex]

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:

[tex]S_n=\dfrac{n}{2}(2a+(n-1)d)\\[/tex]

Putting the values:

[tex]\Rightarrow \dfrac{n}{2} ({2 \times 2 +(n-1)2})\\\Rightarrow \dfrac{n}{2} (4 +2n-2)\\\Rightarrow \dfrac{n}{2} (2n +2)\\\Rightarrow \dfrac{n}{2} \times 2(n +1)\\\Rightarrow n(n +1)[/tex]

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

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