Resources

Resources

Identify arithmetic and geometric series

Example: Find the arithmetic, geometric, and harmonic means of

1

2

3

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5

96,-24,6 ext{ is this geometric or arithmetic} ext{?}

What kind of sequence is this?

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148, 135, 122, 109, \dots

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What kind of sequence is this?

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232, 220, 210, 202, \dots

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What kind of sequence is this?

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167, 151, 135, 119, \dots

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What kind of sequence is this?

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182, 162, 142, 122, \dots

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What kind of sequence is this?

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136, 136, 136, 136, \dots

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What kind of sequence is this?

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593, 593, 593, 593, \dots

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What kind of sequence is this?

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665, 665, 665, 665, \dots

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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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10 \sqrt{2}, \quad 10, \quad 5 \sqrt{2}, \quad \ldots

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\frac{3 \sqrt{2}}{2}

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3 \sqrt{2}

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\frac{\sqrt{2}}{2}

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\sqrt{2}

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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8,-24,72, \ldots

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32

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-32

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-\frac{1}{3}

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-3

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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-6 x-6, \quad-8 x-2, \quad-10 x+2, \quad \text {.. }

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-2 x-4

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-2 x+4

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2 x-4

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2 x+4

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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7,1,-5, \ldots

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\frac{1}{7}

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-6

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7

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6

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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8,12,16, \ldots

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\frac{2}{3}

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\frac{3}{2}

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-4

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4

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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x-3, \quad 2 x-3, \quad 3 x-3, \quad \text {.. }

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-x

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-1

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1

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x

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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9,-45,225, \ldots

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-5

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-54

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-\frac{1}{5}

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54

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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-2 x-6, \quad-2 x-8, \quad-2 x-10, \quad \ldots

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2

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14

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-2

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-14

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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1, \quad \sqrt{3}, \quad 3, \quad \ldots

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\frac{\sqrt{3}}{3}

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\frac{2 \sqrt{3}}{3}

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\sqrt{3}

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2 \sqrt{3}

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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7,14,21, \ldots

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\frac{1}{2}

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-7

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7

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2

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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2 \sqrt{2}, \quad 6, \quad 9 \sqrt{2}, \quad \ldots

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\frac{\sqrt{2}}{2}

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3 \sqrt{2}

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\sqrt{2}

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\frac{3 \sqrt{2}}{2}

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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3,-3,-9, \ldots

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-1

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-1

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-6

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6

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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5,1,-3, \ldots

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-4

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\frac{1}{5}

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4

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5

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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5,15,25, \ldots

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\frac{1}{3}

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3

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-10

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10

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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1,5,9, \ldots

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-4

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\frac{1}{5}

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4

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5

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

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5 x-2, \quad 5 x+2, \quad 5 x+6, \quad \text {.. }

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0

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0

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4

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-4

Find the common ratio of the geometric sequence

-18,-36,-72, \ldots

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Which recursive sequence would produce the sequence

3,13,63, \ldots

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a_{1}=3

a_{n}=5 a_{n-1}-2

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a_{1}=3

a_{n}=-5 a_{n-1}+6

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a_{1}=3

a_{n}=-2 a_{n-1}+5

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a_{1}=3

a_{n}=6 a_{n-1}-5