Geometric Sequences

Geometric Sequences

and Exponential Functions

Multiple Choice

What is an arithmetic sequence?

A sequence made by ______ the ____ value each time.

• adding; first

• multiplying; same

• adding; same

• multiplying; first

Open Ended

Write the next three terms in this sequence.

{1, 4, 7, ...}

Multiple Choice

Arithmetic sequences change by ADDING the SAME value each time.

Which of these sequences are arithmetic sequences?

a) {3, 6, 12, 24, ...}

b) {32, 16, 8, 4, ...}

• Only a

• Only b

• Both a & b

• Neither

Open Ended

Write the next three terms in this sequence.

{3, 6, 12, 24...}

Open Ended

Write the next three terms in this sequence.

{32, 16, 8, 4, ...}

Multiple Choice

Sequences that increase or decrease by MULTIPLYING the previous term by a fixed number are called _________ sequences.

• arithmetic

• geometric

• logarithmic

• mathematic

Multiple Choice

This fixed number is called the common _____.

• area

• difference

• ratio

• variable

How do I find the COMMON RATIO?

• Divide any term by the term before it (previous term).

• r = a_n / a_n-1

• r = common ratio

• a_n = n^th term

• n > 2

Open Ended

Find r, the common ratio.

{3, 9, 27, 81, ...}

Open Ended

Find r, the common ratio.

{-252, 126, -63, 31.5, ...}

Arithmetic vs. Geometric Sequences

Compare & Contrast

Arithmetic Sequences

• Increase/decrease by the common difference, d

• Values change by ADDITION

• a_n = a₁ + (d - 1)

Geometric Sequences

• Increase/decrease by the common ratio, r

• Values change by MULTIPLICATION

• a_{n =} ar^n-1

Classifying Sequences

Determine if each sequence is arithmetic, geometric, or neither.

Multiple Choice

{2, 7, 12, 17, 22, ...}

• arithmetic

• geometric

• neither

Multiple Choice

{-6, -3.7, -1.4, 0.9, ...}

• arithmetic

• geometric

• neither

Multiple Choice

{2, 6, 18, 54, 162, ...}

• arithmetic

• geometric

• neither