Question

An amphitheater has 50 seats in the first row of the center section. Each row behind the first row gains ten additional seats. How many seats are there in the 20th row in the center section?

Answer 1

Answer: 240

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Step-by-step explanation:

• 1st row = 50 seats
• 2nd row = 50+10 = 60 seats
• 3rd row = 60+10 = 70 seats

and so on.

We have the arithmetic sequence 50, 60, 70, ...

• 
  `a_1` = 50 = first term
• d = 10 = common difference

We'll use the formula below to also plug in n = 20 to determine how many seats there are in the 20th row.

`a_n = a_1 + d(n-1)\\\\a_n = 50 + 10(n-1)\\\\a_(20) = 50 + 10(20-1)\\\\a_(20) = \boldsymbol{240}\\\\`

There are 240 seats in the 20th row of the center section.