Lesson: Recursive Formulas for Arithmetic & Geometric Sequences

Lesson: RECURSIVE Formulas

Arithmetic and Geometric Sequences

Recursive Equations

• A recursive formula names the first term (or any other term) and how to get from one term to the next.

Things to know first...

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a_n= the term we are looking for
a_n-1= the previous term
d = common difference

Recursive Formula: a_n=a_n-1 + d

We have formulas to help find those terms that are further along the sequence.

Notes Continued:

Multiple Choice

Given the sequence 2, 8, 14, 20, 26, ... What is the common difference?

• 2

• 4

• 6

• 8

Multiple Choice

Write the recursive formula for 6, 17, 28, 39, 50....

• a_n=a_n-1+11

  a₁=6

• a_n=a_n-1-4

  a₁=6

• a_n=a_n-1+9

  a₁=6

• a_n=a_n-1+6

  a₁=6

Multiple Choice

What is the common ratio for the sequence:

28, 14, 7, 3.5...

• 2

• 1/2

• -14

• -7

Multiple Choice

Write a recursive formula for the following sequence:

16,8, 4, 2,...

• a₁=16

  a_n=a_n-1 (2)

• a₁=16

  a_n=a_n-1 (1/2)

• a₁=16

  a_n=a_n-1 + (1/2)

• a₁=16

  a_n=a_{n-1 +} (2)