Recursive Equations: Unit 1 Test Review

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

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

Tags

CCSS.HSF.BF.A.2

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

• a_n = a_n-1 + 16
  a₁=17
• a_n = a_n-1 - 17
  a₁=17
• a_n = a_n-1 - 15
  a₁=17
• a_n = a_n-1 - 16
  a₁=17

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

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

Tags

CCSS.HSF.BF.A.2

Given the recursive formula below, find the explicit formula.

a₁= 6

a_n = a_n-1 + 5

• a_n = 6 + 5n

• a_n = 1 + 5n

• a_n = 11 + 5n

• a_n = -4 + 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

• a_n = -6 +5n

• a_n = -6 + 11n

Which of the following recursive formulas represents the given sequence.

7, 14, 28, 56, 112, ...

• $a_1=7$ , $a_n=a_{\left(n-1\right)}+7$

• $a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot7$

• $a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot2$

• $a_1=7$ , $a_n=a_{\left(n-1\right)}+14$

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

Determine the 3rd term of the sequence.
 $a_1=5$  

 $a_n=2\cdot a_{n-1}-1$  

• 14

• 13

• 17

• 16

Given the recursive formula, find the explicit form

a_n = a_n-1 - 5

a₁ = 22

• a_n = 22 - 5(n-1)

• a_n = 22 +5 (n-1)

• a_n = -5 + 22n

• a_n = 22-5n

Determine the first 3 terms of the following sequence. $t_n=3\cdot t_{n-1}$  ,  $t_1=-3$  

• -3, 9, 27

• -3, -9, -27

• -3, -6, -9

• -3, 6,9

 $f\left(n\right)=\ \ 24\ \left(\frac{1}{2}\right)^{\left(n-1\right)}$  Given the explicit formula, find the recursive equation.

•  $a_1=24$  ,  $a_n=\frac{1}{2}\cdot a_{n-1}$   

•  $a_1=24$ ,  $a_n=2\cdot a_{n-1}$  
  

•  $a_1=12,\ a_n=\frac{1}{2}\cdot a_{n-1}$  
  

•  $a_1=48,\ a_n=\frac{1}{2}\cdot a_{n-1}$