SOLUTION: The Greek theater has 50 seats in the first row. Each row behind the first-row gains 4 additional seats. How many seats are there in the 10th row?

Question 1186206: The Greek theater has 50 seats in the first row. Each row behind the first-row gains 4 additional seats. How many seats are there in the 10th row?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.


Simply, you should add 9 times 4 seats to 50 seats


    the number of seats in 10th row = 50 + 4*9 = 50 + 36 = 86.


The sequence of numbers, presenting seats in each row is

    50. 54, 58, 62, . . . 


each time you add 4 seats to the previous number.


It is so called arithmetic progression.


Its first term is 50.  Its common difference is 4.



The formula for the n-th term is   = .



For the 10th term (10th row) you have, according the formula,   = 50 + 4*(10-1) = 86,

exactly the same number as we obtained above.

Solved and explained.

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

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.

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".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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