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

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.

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.

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