Question

The right side of the orchestra section of the Nederlander Theater in New York City has 19 rows, and the last row has 27 seats. The number of seats in each row increases by 1 as you move toward the back of the section. How many seats are in this section of the theater. a. 342 seats c. 27 seats b. 293 seats d. 513 seats

Answer 1

27+26+25+24+23+22+21+20+19+18+17+16+15+14+13+12+11+10+9=342
A.342 seats.

Answer 2

342 seats

Explanation:

Given : Theater has 19 rows and the last row has 27 seats. The number of seats in each row increases by 1 as you move toward the back of the section.

To Find: How many seats are in this section of the theater.

Solution:

Since we are given that each row increases by 1 seat

So, we can use arithmetic progression

So, d = 1

No. of rows n = 19

The last row i.e. row 19 has 27 seats

nth term of A.P. =
`a_n=a+(n-1)d`

a is the first term

Substitute n = 19

So,
`a_(19)=a+(19-1)(1)`

`a_(19)=a+18`

Since row 19 has 27 seats

So,
`27=a+18`

`27 -18=a`

`9=a`

Now we are supposed to find the number of seats in the theater.

So, Sum of first n terms in A.P. =
`S_n=(n)/(2)(a+a_n)`

Substitute n =19

`S_(19)=(19)/(2)(9+27)`

`S_(19)=342`

Hence there are 342 seats in the theater.