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In the seating for a concert, the first row has 10 chairs. Every row after that has 2 more chairs. 7. What is the explicit formula that models this situation? 8. How many chairs are in row 20?​

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Answer:

7. c(n) = 10 +2(n -1)

8. c(20) = 48

Explanation:

7. Your arithmetic sequence has first term a1=10 and constant difference d=2. The explicit formula for terms of an arithmetic sequence is ...

an = a1 +d(n -1)

If we use c(n) as the function name for the function giving the number of chairs in row n, then we can fill in the numbers we know to get ...

c(n) = 10 + 2(n -1)

__

8. Evaluating the function when n=20, we find ...

c(20) = 10 +2(10-1) = 10 +2·19 = 10 +38

c(20) = 48

There are 48 chairs in row 20.

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