Geometric Sequences and Series

Geometric Series

By Ryan Kripp

​Determine if a series is Geometric

​2, 5, 10, 17

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2, 6, 18, 54​

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Multiple Choice

State if each sequence is geometric.

-1, -4, -16, -64

• Yes

• No

Multiple Choice

State if each sequence is geometric.

4, 16, 36, 64

• Yes

• No

Multiple Choice

State if the sequence is geometric.

1, 9, 25, 49

• Yes

• No

Multiple Choice

State if the sequence is geometric.

1, -3, 9, -27

• Yes

• No

Find the Common Ratio

-4, 24, -144, 864

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​

-1, 6, -36, 216​

​

Some text here about the topic of discussion

Multiple Choice

Find the common ratio.

3, 15, 75, 375

• -2

• 5

• -5

• 2

Multiple Choice

Find the common ratio.

-2, -4, -8, -16

• 5

• -4

• 2

• -2

Multiple Choice

Find the common ratio.

1, -6, 36, -216

• -6

• 6

• 2

• 3

Multiple Choice

Find the common ratio.

-2, 6, -18, 54

• -1/4

• -3

• -4

• 4

​Find the Explicit formula a_n=a₁(r)^n-1

-2, -8, -32, -128

​

-1, 6, -36, 216​

​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Find the explicit formula.

-4, -12, -36, -108

• $$a_n=-5\left(3\right)^{\left(n-1\right)}$$  

• $$a_n=-5\left(\frac{1}{3}\right)^{\left(n-1\right)}$$  

• $$a_n=5\left(-3\right)^{\left(n-1\right)}$$  

• $$a_n=-4\left(3\right)^{\left(n-1\right)}$$  

Multiple Choice

Find the explicit formula.

-3, 18, -108, 648

• $$a_n=-3\left(-6\right)^{\left(n-1\right)}$$  

• $$a_n=24\left(6\right)^{\left(n-1\right)}$$  

• $$a_n=4\left(6\right)^{\left(n-1\right)}$$  

• $$a_n=-4\left(-6\right)^{\left(n-1\right)}$$  

Multiple Choice

Find the explicit formula.

4, 12, 36, 108

• $$a_n=5\left(-\frac{2}{3}\right)^{\left(n-1\right)}$$  

• $$a_n=-4\left(\frac{2}{3}\right)^{\left(n-1\right)}$$  

• $$a_n=4\left(3\right)^{\left(n-1\right)}$$  

• $$a_n=4\left(\frac{1}{3}\right)^{\left(n-1\right)}$$  

Multiple Choice

Find the explicit formula.

-1, -5, -25, -125

• $$a_n=2\left(-5\right)^{\left(n-1\right)}$$  

• $$a_n=2\left(4\right)^{\left(n-1\right)}$$  

• $$a_n=-1\left(5\right)^{\left(n-1\right)}$$  

• $$a_n=-1\left(-5\right)^{\left(n-1\right)}$$  

​Find the 8th Term​

-3, -9, -27, -81

​

​

4, -16, 64, -256​

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Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Find the 8th term.

2, -8, 32, -128

• -32768

• -49152

• -3/16384

• 196608

Multiple Choice

Find the 8th term.

-2, -12, -72, -432

• -1171875

• 234375

• -559872

• -839808

Multiple Choice

Find the 8th term.

-4, 12, -36, 108

• 8748

• -1/6561

• -2916

• -729

Multiple Choice

Find the 8th term.

-4, -12, -36, -108

• -2187

• -729

• -6562

• -8748