Recursive and Explicit Patterns

A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern. 
What is the meaning of a_4?

• There are 60 seats in the first row
• There are 84 seats in the fourth row
• There are 82 seats in the fourth row
• There are 76 seats in the row before the fourth row

A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern.

What is the explicit form of this sequence?

• f(x) = 60(8)^x , where x = 0,1,2,...

• a_n = 60(8)ⁿ, where n = 0,1,2,...

• a_n = 8n + 60, where n = 0,1,2,..

• a_n = 60 + 8(n-1), where n= 1,2,3,...

A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern.  How many seats are in the 6th row?

• 100
• 84
• 92
• 52

Find the recursive form of the sequence

-56, -60, -64, .......

• a_n+1 = a_n - 56, n = 1,2,3,...

  a₁ = -4

• a_n+1 = a_n - 4, n=1,2,3,...

  a₁ = -56

• a_n+1 = a_n - 4, n=0,1,2,...

  a₁=-56

• a_n+1 = a_n - 56, n = 0,1,2,...

  a₁ = -4

Write the recursive formula for 6, 17, 28, 39, 50....

• a_n=a_n-1+11
  a₁=6
• a_n=a_n-1-4
  a₁=6
• a_n=a_n-1+9
  a₁=6
• a_n=a_n-1+6
  a₁=6

Given the recursive formula, find the first four terms:

a_n+1 = a_n + 5

a₁ = -16

• -16, -21, -26, -31

• 5, -11, -27, -43

• -16, -80, -500, -200

• -16, -11, -6, -1

Identify the common difference.
97, 86, 75, 64, ...

• 8
• 11
• -11
• -8

Create the explicit formula for the sequence:

2, 8, 14, ...

• a_n = 2 + 6(n-1), where n = 1,2,3,...

• a_n = -6 + 6(n-1), where n = 1,2,3,...

• a_n = 6(n-1) - 4, where n = 1,2,3,...

• a_n = 4 - 6(n-1), where n = 1,2,3,...

Given the recursive formula, find the first four terms:
a_n+1 = a_n + 5
a₁ = -16

• -16, -21, -26, -31
• 5, -11, -27, -43
• -16, -80, -500, -200
• -16, -11, -6, -1

Find the 16th term.

• 16
• 31
• 25
• 35