# Math Help - word problem

1. ## word problem

1. A theatre has 20 rows of seats. There are 15 seats in the first row, 17 seats in the second row, and each successive row of seats has two more seats than the previous row.
a. calculate the number of seats in the 20th row.
b. Caculate the total number of seats.

2. A factory makes calculators. Over a long period of time, 2% of them are found to be faulty. A random sample of 100 calculators is tested.
a. Write down the expected number of faulty calculators in the sample.
b. Find the probability that three calculators are faulty.
c. Find the probability that more than one calculator is faulty.

Thanks ffor the help!!

2. Hello, miley_22!

The first one involves an Arithmetic Progression.

1. A theatre has 20 rows of seats. There are 15 seats in the 1st row, 17 seats in the
2nd row, and each successive row of seats has two more seats than the previous row.

a. Calculate the number of seats in the 20th row.
The $n^{th}$ term of an Arithmetic Progression is:

. . $a_n \;=\;a_1 + (n-1)d$

where: . $a_1 = \text{1st term},\;d = \text{common difference},\:n = \text{no. of terms.}$

We have: . $a_1 = 15,\;d = 2,\;n = 20$

Therefore: . $a_{20} \;=\;15 + 19(2) \;=\; 53$

b. Caculate the total number of seats.
The sum of the first $n$ terms of an Arithmetic Progression is:

. . $S_n \;=\;\frac{n}{2}\bigg[2a_1 + (n-1)d\bigg]$

Therefore: . $S_{20} \;=\;\frac{20}{2}\bigg[2(15) + 19(2)\bigg] \;=\;680$