SOLUTION: The theater has 35 seats in the 1st row, 45 in the 2nd row and 55 in the 3rd row and so on. A. What is the common difference? B. How many seats are there in the 25th row? C. W

Algebra ->  Sequences-and-series -> SOLUTION: The theater has 35 seats in the 1st row, 45 in the 2nd row and 55 in the 3rd row and so on. A. What is the common difference? B. How many seats are there in the 25th row? C. W      Log On


   



Question 1088620: The theater has 35 seats in the 1st row, 45 in the 2nd row and 55 in the 3rd row and so on.
A. What is the common difference?
B. How many seats are there in the 25th row?
C. Which row has 205 seats?

Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
The theater has 35 seats in the 1st row, 45 in the 2nd row and 55 in the 3rd row and so on.

A. What is the common difference?               The common difference is d = 45 - 35 = 10.

B. How many seats are there in the 25th row?    a%5B25%5D = a%5B1%5D + (25-1)*d = 35 + 24*10 = 35 + 240 = 275.

C. Which row has 205 seats?                     a%5Bn%5D = a%5B1%5D + (n-1)*d = 35 + 10*(n-1) = 205.  
                                                Solve it for n: 10(n-1) = 205-35 = 170  ====>  n-1 = 17  ====>  n = 18.

                                                Answer. 18-th row has 205 seats.

On arithmetic progressions see the lessons in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".