Question

The first row of a section in a stadium has 10 seats. The second row has 11 seats. The third row has 12 seats. This pattern continues and the section has 24 rows.

How many seats are in this section?

Answer 1

Answer:

516

Step-by-step explanation:

Answer 2

You can use the formula for sum of consecutive integers.

There are total 516 seats.

How to calculate sum of consecutive numbers?

Suppose the numbers are a, a+1, a+2, ... , a+n

Then you write their sum as S

Then we have:

$S = (a) + (a+1) + (a+2)+ ... + (a+n)\\S = (a+n) + (a+n-1) + (a+n-2) + .... + (a)$

I just wrote the numbers in reverse.

Now if you add both the equations term by term, you will get:

$2S = (a + a + n) + (a+1 + a+n-1) + (a+2 + a+n-2) + ... + (a+n + a)\\2S = (2a+n) + (2a+n) + ... (2a+n) \text{(\: n +1 times)}\\\\2S = (n+1)(2a+n)\\\\S = \dfrac{(n+1)(2a+n)}{2}$

Using this formula to get the total number of seats

Since the seats are like 10, 11, 12,  .... (24 times), thus we have:

a = 10,

n+1 = 24 or n = 23

Thus, the sum of those numbers which denotes total seat is:
$S = \dfrac{(2 \times 10 + 23)(23 + 1)}{2}\\\\S = \dfrac{43 \times 24}{2}\\\\S = 43 \times 12 = 516$

Thus, There are total 516 seats.

Learn more about sum of consecutive integers here:

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