SOLUTION: A theatre is set up in such a way that there are 20 seats in the first row and 4 additional seats in each consecutive row. The last row has 144 seats. How may rows are there in t

Question 55015: A theatre is set up in such a way that there are 20 seats in the first row and 4 additional seats in each consecutive row. The last row has 144 seats. How may rows are there in the theatre?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You could set up a table to find the general formula that relates the number of seats in each row:
Let the row number be n.
The first row: n = 1 there are 20 seats.
The second row n = 2 there are 20 + 4 seats.
The third row n = 3 there are 20 + 2(4) seats. Notice that 2 = n-1
The fourth row n = 4 there are 20 + 3(4) seats. Notice that 3 = n-1
.
.
.
The nth row n = n there are are 20 + (n-1)4 seats.
In the last row there are 144 seats so we'll set 20 + (n-1)4 = 144 and solve for n.
20 + (n-1)4 = 144 Simplify and solve for n.
20 + 4n - 4 = 144
16 + 4n = 144 Subtract 16 from both sides.
4n = 128 Divide both sides by 4.
n = 32 rows.
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