Geometric Series

Geometric Series

By Steven Giesting

Multiple Select

Identify all of the sequences that are geometric 

• 2, 10, 50, 250, . . .

• 3, 6, 9, 12, . . .

• 1, 1, 2, 3, 5, . . .

• $$100,\ 50,\ 25,\ \frac{25}{2},\ \frac{25}{4},\ .\ .\ .$$  

Fill in the Blank

Find the sum of the following series

3 + 7 + 11 + . . . + 59

​Example 1: Find the sum of the series

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4 + 12 + 36 + 108 + 324 + ​972 + 2916

​Example 2: Find the sum of the series

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-15 + 30 - 60 + 120 - 240 + 480​

​a₁ = - 15

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r = -2

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n = 6​

​Example 3: Find the sum

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Fill in the Blank

Evaluate the sum of the finite geometric series

1 + 2 + 4 + . . . + 128

​Example 3

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Does the series converge or diverge? If it converges, find its sum

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Fill in the Blank

$$1+\frac{1}{4}+\frac{1}{16}\ +\ .\ .\ .\$$  Find the sum of the infinite geometric series, if it exists

Multiple Choice

Does the following series converge or diverge?

$$\frac{1}{4}-\frac{3}{8}+\frac{9}{16}-\frac{27}{32}+.\ .\ .$$  

• converge

• diverge