4. Explicit to Recursive and Back

Type of sequence: ​ (a)  

This sequence has a common ​​ (b)   ​

The second term in the sequence is ​ (c)  

• geometric
• ratio
• 10
• arithmetic
• difference
• 7
• 2.5
• 3

Tags

AI.9.12.C

Which is the recursive formula describing this sequence?

• g_n = 2•3^n-1

• g₁ = 2

  g_n = 3 • g_n-1

• t_n = 2 + (n - 1)3

• a₁ = 2

  a_n = a_{n - 1} + 4

Tags

AI.9.12.D

g₅ = 3888 , and g₃ = 108.

The common ratio is ​ (a)   and the first term is ​ (b)  

• 6
• 3
• 1/2
• 1/6
• 0
• 1
• 160
• 2

Tags

AI.9.12.D

In a sequence of numbers, a₄ = 648, a₅ = 1944, a₆ = ​ 5832.

a₁ = ​ (a)  

a_n = (​ (b)   ) • a_{n - 1}

• 24
• 3
• 8
• 0
• 1/3
• 1296

Tags

AI.9.12.C

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 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