4. Translate Between Explicit and Recursive

Tables with Recursive and Explicit Formulas

Multiple Choice

Which table of values fits the explicit function $$f\left(x\right)=2\cdot3^x$$ ?

Remember 2 is the 0 term

Multiple Choice

Which table could fit with the recursive rule $$f\left(n\right)=f\left(n-1\right)\cdot2$$ ?

Remember 2 is the first term.

Multiple Choice

What is the recursive function for the sequence?

• f(1) = 6, f(n) = f(n-1) + 4

• f(1) = 4, f(n - 1) + 6

• f(n) = 4n + 2

• f(n) = 4 + 6(n - 1)

Multiple Choice

What is the explicit function for the sequence?

• f(1) = 6, f(n) = f(n-1) + 4

• f(1) = 4, f(n - 1) + 6

• f(n) = 4n + 2

• f(n) = 4 + 6(n - 1)

Multiple Choice

What is the recursive function for the sequence?

• $$f\left(0\right)=3,\ f\left(n\right)=4\cdot f\left(n-1\right)$$

• $$f\left(0\right)=3,\ f\left(n\right)=4+f\left(n-1\right)$$

• $$f\left(n\right)=3\cdot4^x$$

• $$f\left(n\right)=4\cdot3^x$$

Multiple Choice

What is the explicit function for the sequence?

• $$f\left(n\right)=3n+4$$

• $$f\left(n\right)=4n$$

• $$f\left(n\right)=3\cdot4^x$$

• $$f\left(n\right)=4\cdot3^x$$

Recursive to Explicit and Recursive to Explicit

​Recursive to Explicit

​Geometric Sequence

Multiple Choice

Given the recursive formula, write the explicit formula for the geometric sequence.

$$a_1=6$$  
$$a_n=5\cdot a_{n-1}$$  

• $$a_n=5\cdot6^{n-1}$$  

• $$a_n=6\cdot5^{n-1}$$  

• $$a_n=6+5\left(n-1\right)$$  

• $$a_n=5+6\left(n-1\right)$$  

Drag and Drop

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

a₁ = ​

Placeholder

a_n = (​

Placeholder

) • a_{n - 1}

Drag these tiles and drop them in the correct blank above

24

3

8

0

1/3

1296

Multiple Choice

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

Multiple Choice

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 

​Arithmetic Sequence

​Work Backwards for Recursive to Explicit

​g(n)= -13 +6n

​The first term is -19, so to find the 0 term add 6 to get -13

Multiple Choice

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

• y = 9 + 2n
• y = 7 + 2n 

Multiple Choice

Given the explicit formula for a geometric sequence find the recursive formula.

$$a_n=-3\cdot\left(\frac{1}{2}\right)^{n-1}$$  

• $$a_n=a_{n-1}\cdot-2,\ a_1=4$$  

• $$a_n=a_{n-1}\cdot-\frac{1}{2},\ a_1=4$$  

• $$a_n=a_{n-1}\cdot\frac{1}{2},\ a_1=-4$$  

• $$a_n=a_{n-1}\cdot\frac{1}{2},\ a_1=-3$$  

Multiple Choice

The explicit formula is used to find a specific term in a sequence.

• True
• False

Multiple Choice

The recursive formula can only be used if you know the previuos term

• True
• False