Question

Denise is designing the seating arrangement for a concert an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Help Denise plan the rest of the seating by solving for how many seats are in row 18. Then explain to Denise how to create an equation to predict the number of seats in any row. Show your work, and use complete sentences.

Answer 1

This is an Arithmetic Progression with 1st term 11 and common difference d=6

Number of Rows     Number of seats      Common difference " d" 
-----------------------     -----------------------     -------------------------------------
1st                                  a₁     = 11                                 
2nd                                 a₁+d =17               d =2nd - 1st = 6
3rd                                  a₁ +2d = 23           d =3rd - 2nd = 6
4th                                  a₁ +3d = 29            d= 4th - 3rd = 6
-------------------------------------------------------------------------------
nth ROW                         a(n) = a₁ + (n-1)d
18th ROW                       a₁₈ =   11 + (18-1).6 = 11+(17)(6) = 113 

General equation to predict the number of seat an the nth row:
Number of seats in nth row = a₁ + (n-1).d