Explicit and Recursive Functions

Find the next three terms:
5, 8, 11, 14...

• 16, 19, 22
• 17, 19, 21
• 17, 20, 23
• 16, 18, 20 

Given the recursive formula below, find the first five terms.  
u₁ = 3
u_n = u_n-1 + 2
where n ≥ 2

• 3, 5, 7, 9, 11
• 5, 7, 9, 11, 13

Given the first five terms, write the recursive formula.
15, 12, 9, 6, 3 ....

• u₁ = 15
  u_n = u_n-1 + 3
• u₀ = 15
  u_n = u_n-1 + 3
• u₁ = 15
  u_n = u_n-1 - 3 
• u₀ = 15
  u_n = u_n-1 - 3

Given the recursive formula below, find the explicit formula.  
a₀ = 1
a_n = a_n-1 + 5

• a_n = 6 + 5n
• a_n = 1 + 5n

Given the sequence below, write the explicit formula.
3, 8, 13, 18 ... 

• u_n = 3 + 5n
• u_n = -2 + 5n

Given the recursive formula below, find the explicit formula.  
a₁ = 5
a_n = a_n-1 - 6

• a_n = 5 - 6n 
• a_n = 11 - 6n 

Given the explicit equation below, write the linear equation.
u_n = 7 - 3n

• y = 7 - 3x
• y = 10 - 3x 

How does a linear equation relate to the explicit formula?  

• the initial value is the common difference
• the initial value is the slope
• the initial value is the y-intercept
• the y-intercept is u₁

How does a linear equation relate to the explicit formula?  

• the slope is the common difference
• the y-intercept is the common difference
• the two are not related
• the slope is u₁

Given the recursive formula below, write the linear equation.
a₁ = 9
a_n = a_n-1 + 2

• y = 9 + 2n
• y = 7 + 2n