Question

You are arranging chairs for a play and the number of chairs per row keeps increasing by 2. If the first row had 10 chairs, the second row 12 chairs, third row 14 chairs and so on, how many total chairs are needed for 10 rows?

Answer 1

Answer:

190 chairs

Step-by-step explanation:

-This is an arithmetic progression with the first term a=10, the common difference is d=2 and the number of terms n=10.

-The sum of n terms in the progression can be calculated as follows:

$S_n=0.5n(a_1+a_n)$

Where

$S_n$ is the sum of the progression's terms.

$a_1, \ a_n$ are the first and last terms of the progression.

#We calculate $a_n=a_{10}$ as below:

$a_n=a_1+d(n-1)\\\\a_{10}=10+2(10-1)\\\\=28$

#We then substitute to calculate the sum of the terms:

$S_n=0.5n(a_1+a_n)\\\\=0.5\times 10(10+28)\\\\=190$

Hence, 190 chairs are needed for the 10 rows.