Arithmetic and Geometric Sequences

Create the formula for the arithmetic sequence:
5, 105, 205, 305...
then find the 22nd term.

• a₂₂ = 1905

• a₂₂ = 2105

• a₂₂ = 2195

• a₂₂ = 2305

Create the formula for the geometric sequence:
-3, -6, -12, -24...
then find the 12th term.

• a₁₂ = -6144

• a₁₂ = 6144

• a₁₂ = -6234

• a₁₂ = 6234

900, 450, 225, 112.5

• Geometric sequence with a common ratio of 1/2

• Geometric sequence with a common ration of 2

• Arithmetic sequence with a common difference of 450

• Common difference of 2

A child on a swing is let go from a vertical height so that the distance he travels in the first back - and - forth swing is exactly 9 feet.  If each swing decreases the distance by 85 % write a geometric series that expresses the distance the child travels in feet. 

• a_n = 9 (.85)^n-1

• a_n = 9 (.15) ^{n - 1}

• a_n = (.85) (9) ^n-1

The first two numbers in a sequence h are h₁=2 and h₂=6.

If h is an arithmetic sequence, write the recursive definition for the sequence. Then write the first 5 terms of the arithmetic sequence

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The first two numbers in a sequence h are h₁=2 and h₂=6.

If h is a geometric sequence, write the recursive equation for the geometric sequence. Then write the first five terms of the sequence.

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Find the next four terms of the arithmetic sequence 16, 24, 32,...

• 40, 48, 56, 64

• 36, 40, 44, 48

• 35, 40, 45, 50

• 40, 44, 50, 56

Write an equation to define k recursively.

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What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

• 1024, 2048, 4096

• 32, 8, 2

• 64, 32, 16

• 92, 66, 38

Fill in the blank of the geometric sequence,

3, 6, _, 24