Geometric Sequences

Presentation

•

Mathematics

•

9th Grade

•

Medium

•

CCSS

HSF.BF.A.2

Standards-aligned

Shayna Richter

Used 364+ times

FREE Resource

6 Slides • 12 Questions

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, ...}

Type response here

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...}

Type response here

Open Ended

Write the next three terms in this sequence.

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

Type response here

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, ...}

Type response here

Open Ended

Find r, the common ratio.

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

Type response here

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

Geometric Sequences

and Exponential Functions

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