Applying and analysing functions

 $f\left(n\right)=\left(-2\right)^n$  
 $f\left(3\right)=?$  

• 6

• 8

• -8

• -6

The formula for a sequence that uses operations on a previous term to find the next term is called a/an:

• Explicit Formula

• Recursive Formula

• Arithmetic Formula

• Geometric Formula

• the final term in the sequence

• first term

• Nth term, where n>1

• previous term

 $f\left(n\right)=12\left(3\right)^{n-1}$  
Which recursive equation below would describe the same set of values as the explicit equation above?

•  $f\left(0\right)=12\ ;\ f\left(n\right)=3f\left(n-1\right)$  

•   $f\left(0\right)=3\ ;\ f\left(n\right)\ =12f\left(n-1\right)$  

•  $f\left(1\right)=12\ ;\ f\left(n\right)\ =3f\left(n-1\right)$  

•  $f\left(1\right)=3\ ;\ f\left(n\right)=12f\left(n-1\right)$  

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

Find the recursive function that fits this table.

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Which formula defines the sequence ƒ(1) = 2, ƒ(2) = 6, ƒ(3) = 10, ƒ(4) = 14, ƒ(5) = 18?

• A. f(1) = 2, f(n) = 6 + f(n-1) for n ≥ 2

• B. f(1) = 2, f(n) = 4 + f(n-1) for n ≥ 2

• C. f(1) = 2, f(n) = 2 + f(n − 1) for n ≥ 2

• D. f(1) = 6, f(n) = 4 + f(n − 1) for n ≥ 2

Write the recursive function for the given quadratic table.

• f(1)=0, f(x)=f(x-1)+4x+1

• f(1)=0, f(x)=f(x-1)+4x

• f(1)=0, f(x)=f(x-1)+4x+5

• f(1)=0, f(x)=f(x-1)+4x+10