Question

You have been asked to set up chairs for the school concert. The first row will have 10 seats, and each additional row has 4 seats more than the previous row. What is the total number of chairs needed to set up 25 rows?

Answer 1

Answer:

The total number of chairs needed to set up 25 rows is 1450 chairs

Explanation:

Given:

first row = 10 seats

each new row has an additional 4 seats than the previous

To find:

total number of chairs required to set up 25 rows

1st row = 10 seats

2nd row = 10 = 4 = 14 seat

3rd row = 14 + 4 = 18 seat

We have a common difference = next row - previous row

common difference = 18 - 14 = 4

To set up 25 rows, we will apply the sum of arithmetic sequence (since we have a common difference).

The formula is given as:

$\begin{gathered} S_n\text{ = }\frac{n}{2}(2a\text{ + \lparen n - 1\rparen d\rparen} \\ \\ a\text{ = 1st term \lparen1st row in this case\rparen = 10} \\ n\text{ = number of terms = 25} \\ d\text{ = common difference = 4} \\ S_n\text{ = S}_{25}\text{ = sum of 25 rows} \end{gathered}$

substitute the values into the formula:

$\begin{gathered} S_{25}\text{ = }\frac{25}{2}(2(10)\text{ + \lparen25 - 1\rparen\lparen4\rparen\rparen} \\ \\ S_{25}\text{ = }\frac{25}{2}(20+24(4)) \\ \\ S_{25}\text{ = }\frac{25}{2}(20+96) \end{gathered}$$\begin{gathered} S_{25}\text{ = }\frac{25}{2}(116) \\ \\ S_{25}\text{ = 1450} \end{gathered}$

The total number of chairs needed to set up 25 rows is 1450 chairs