Geometric Patterns

A1: Lesson 10.2: Geometric Sequence

By Patrick Moseley

Multiple Choice

Given the following sequence:

4, 12, 36, 108, ...

Is there a geometric pattern?

• Yes

• No

Fill in the Blanks

Easy identification of pattern:

Second term divided by the first one. Does this hold up between the rest of the terms?

If yes (common ratio), then r = #.

Given the following sequence:

4, 12, 36, 108, ...

What is the pattern (r = _)?

Multiple Choice

Given the following sequence:

5, 10, 15, 20, ...

Is there a geometric pattern?

• Yes

• No

​Given the following sequence:

5, 10, 15, 20, ...

Is there a geometric pattern?

​

Sometimes...there is NO geometric pattern.​

Multiple Choice

Given the following sequence:

625, 125, 25, 5, ...

If there is a pattern, identify the common ratio.

• Yes, r = -5

• Yes, r = 5

• Yes, r = 1/5

• No Pattern

​Finding specific terms from an geometric sequence:

formula: a_n = a₁ * r^n-1

a₁: first term in the sequence

r: common ratio

n: the term location you want to calculate

Example:

Given: 5, 20, 80, ...

a₁ = 5 and r = ​4

​

Formula: ​a_n=5*4^(n-1)

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Replace the n for the desired term needing to calculate.​

Fill in the Blanks

Given: 5, 20, 80, ...

a₁ = 5 and r = ​4

​

Formula: ​a_n=5*4^(n-1)

^{Calculate a₉ =}

Multiple Choice

Given: -2, 10, -50, ...

What formula would you use to calculate the n^th term?

• a_n = -5 * -2^(n-1)

• a_n = -2 * 5^(n-1)

• a_n = 2 * -5^(n-1)

• a_n = -2 * -5^(n-1)

Fill in the Blanks

Given: -2, 10, -50, ...

Calculate a₉ =

​Scenarios:

The following table shows a car's value for 3 years after it is purchased.

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Writing the equation:

a₁ = 10000 and r = 4/5​

an = 10000 * 4/5^{n - 1}

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​Predict the value of the car after 10 years: $1,342.18​

Fill in the Blanks

A ball is dropped from a height of 500 meters. The table shows the height of each bounce.

Calculate the height of the ball on the 6th bounce (round to the nearest meter):