Question

Drury Lane Theater The Drury Lane Theater has 25 seats in the first row and 30 rows in all. Each successive row contains one additional seat. How many seats are in the

theater?

Short answer

There are 1185 seats in the theater.

Step-by-step solution

Given Information 

Theater has 25 seats in the first row , a1=25

n= 30 rows in all.

Each successive row contains one additional seat. . so d=1

find Sum 

Find out sum using sum formula

$$\begin{gathered} S_n=\frac{n}{2}\left(2a_1+(n-1)d\right) \\ {a}_1=25 \\ n=30 \\ d=1 \\ {S}_{30}=\frac{30}{2}\left(2\left(25\right)+(30-1)1\right) \\ {S}_{30}=\frac{30}{2}\left(50+29\right) \\ {S}_{30}=1185 \end{gathered}$$

There are 1185 seats in the theater.