SOLUTION: a theater has 20 rows of chairs the first row has 10 chairs and each row after that has 2 more seats than the row before it How many total seats are in the theater

Question 1206130: a theater has 20 rows of chairs the first row has 10 chairs and each row after that has 2 more seats than the row before it
How many total seats are in the theater
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.
a theater has 20 rows of chairs the first row has 10 chairs and each row after that
has 2 more seats than the row before it. How many total seats are in the theater?
~~~~~~~~~~~~~~~~~~~~

The series of the chairs in rows is an arithmetic progression.


1-st row has 10 chairs.

The last, 20th row has 10 + (20-1)*2 = 10 + 19*2 = 10 + 38 = 48 chairs.

(use the formula for the n-th term of an AP).



In all, there are   =  =  = 58*10 = 580 chairs.

(use the formula for the sum of the first n terms of an AP).

Solved.

------------------

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

RELATED QUESTIONS
A collection of chairs is set up into 22 rows. The first row has 96 chairs, and each... (answered by Edwin McCravy)

A theater has 30 rows of seat, the first row has 10 seats and each row thereafter has 1... (answered by vouge)

A theater contains 25 rows of seats. The first row contains 25 seats. Each succeeding row (answered by richwmiller)

Chairs are arranged in the hall into 18 short rows and 7 long rows. Each long row has 18... (answered by josgarithmetic,greenestamps,ikleyn,Edwin McCravy)

Find the number of row in a theatre containing 30 seats if the first row has 14 seats and (answered by Believe)

A theatre has 20 rows of chairs . The first row has 16 chairs , the second has 18, the... (answered by dkppathak)

a 40 row theater has 10 seats in the front row. the second row has 11 seats. if each row... (answered by josmiceli)

A large multiplex movie house has many theaters. The largest theater has 37 rows. There (answered by ikleyn)