Recursive and Explicit Formula

Given the recursive formula below, find the first five terms.

u₁ = 3

u_n = u_n-1 + 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

Does this recursive routine model an increase or decrease? U₁ = 1000 U_n+1 = U_n*1.25

• Decrease

• Increase

Identify the rule as recursive or explicit, then find the first 4 terms of the sequence.
a₁ = 100; a_n = a_n-1 - 8

• Explicit; 100, 92, 84, 76

• Recursive; 100, 92, 84, 76

• Explicit; 100, 108, 116, 124

• Recursive; 100, 108, 116, 124

Write a recursive formula for the following sequence: 1, -3, 9, -27,...

• a₁= 1

  a_n= (a_n-1)(-3)

• a₁= 1

  a_n= a_n-1 -4

• a₁= -3

  a_n= (a_n-1)(-3)

• a₁= 1

  a_n= (a_n)(-3)

The image shows the sequence 6.5, 5, 3.5, 2, -0.5, . . . What is the recursive formula for this sequence?

• a_n = a_n-1 + 1.5

• a_n = a_n-1 - 1.5

• a_n = a_n-1 + 6.5

• a_n = a_n-1 -6.5

Given the recursive formula, find the first 5 terms:

• 17, 3, -11, -25, -39

• 17, 31, 45, 59, 73

• 17, 7, -3, -13, -23

• -14, 3, 20, 37, 54

What is the explicit rule for the sequence:
11, 22, 44, 88...

• a_n = 2(11)^n-1

• a_n = 11x2

• a_n = 11(2)^n-1

• a_n+1 = a_{n *} 2;  a₁ = 11

Does this recursive routine model growth or decay, and by what percent?

• Growth, 80%

• Growth, 20%

• Decay, 80%

• Decay, 20%