Recursive Formulas Arithmetic Sequences

Find the common difference.

What is the recursive rule for the sequence:
-2, 12, -72, 432, ...

• a_n = -2(-6)^n-1
  a₁=-2

• a_n =a_n-1 + 10
  a₁=-2

• a_n = -6⋅a_n-1 a₁=-2

• a_n = a_(n-1) - 6 a₁=-2

A formula that requires the computation of all previous terms to find the value of a_n.

• Explicit Formula

• Recursive Formula

• Arithmetic Formula

• Geometric Formula

Given the sequence 30, 40, 50, 60..., which recursive formula describes it?

Recursive formulas are mainly used for providing the ______ and the _____ in an arithmetic sequence.

• first term

  and

  last term

• first term

  and

  common difference

• previous term

  and

  final term

• none of these

Determine whether the sequence in the table is arithmetic, geometric, or neither.

• arithmetic

• geometric

• neither

Common difference or ratio?

What are the missing values?

• Difference = 22, 34

• Difference = 24, 34

• Ratio = 22, 34

• Ratio = 24, 34

Classify each function with its description. f\left(x\right)\ =\ f\left(x-1\right)+1,\ f\left(0\right)=5

• arithmetic, explicit

• arithmetic, recursive

• geometric, explicit

• geometric, recursive

Classify each function with its description. f\left(x\right)\ =\ f\left(n-1\right)+2,\ f\left(1\right)=4

• arithmetic, explicit

• arithmetic, recursive

• geometric, explicit

• geometric, recursive

Find the missing terms of the arithmetic and geometric sequences in the table. Use the formulas.

• 8, 14, 20

• 10, 16, 22

• 12, 18, 24