Question

An auditorium has 20 rows with 10 seats in the first row, 12 in the second, 14 in the third row, and so forth. How many seats are in the auditorium???

Answer 1

Please help

Answer 2

I know that the answer is 580 but i want to know how to solve it using sequences

Answer 3

1. Plot the points in the form \((n, s)\)
Where n = row and s = number of seats in the corresponding row

(1, 10)
(2, 12)
(3, 14)
(4, 16)

and so on

2. Note the relationship between n and s
3(1) + 7 = 10
3(2) + 6 = 12
3(3) + 5 = 14
3(4) + 4 = 16

and so on

3. Notice that the formula becomes
\(3n + 8 - n = s\)

Or simply:
(2n + 8 = s\)

4. Take the sum:
\[\sum_{n=1}^{20}(2n + 8)\]