Geometric Sequence Lesson Sample

Geometric Sequences

Is multiplied or divided by the same value every time

Arithmetic Sequences

​Recursive vs. Explicit

​d = common difference

​Common Difference

​Term 0

Geometric Sequences

​Recursive

​r = common ratio

​Common Ratio

​Term 0

​Explicit

Multiple Choice

What does r represent?

• Radical

• Common difference

• Common ratio

Multiple Choice

Find the common ratio for the geometric sequence.

• 10

• 1/2

• 2

• 4

Multiple Choice

Find the common ratio of the following geometric sequence:

2, -10, 50, -250, ...

• r = -5

• r = 3

• r = 5

• r = -3

Multiple Choice

Is this sequence geometric?

• yes

• no

Multiple Choice

Is the sequence 2, 4, 12, 48,... geometric?

• yes

• no

Multiple Choice

Find the next three terms: 4, 12, 36, 108, ...

• 324, 972, 2916

• 972, 2916, 8748

• 405, 1215, 3645

Multiple Choice

Which formula is a recursive equation for geometric sequences?

• f(n) = f(n-1) + d, f(1) = __

• f(n) = f(n-1) * r, f(1) = __

• f(n) = f(1) + d(n-1)

• f(n) = f(1) * r^n-1

Multiple Choice

Write a recursive formula for the following sequence:

16,8, 4, 2,...

• f(1)=16

  f(n)=2f(n-1)

• f(1)=16

  f(n)=0.5f(n-1)

• f(1)=16

  f(n)=f(n-1) + 0.5

• f(1)=16

  f(n)=f(n-1) - 8

Multiple Choice

Which of the following recursive formulas represents the given sequence.

7, 14, 28, 56, 112, ...

• f(n) = f(n-1) + 7, f(1) = 7

• f(n) = f(n-1) * 7, f(1) = 7

• f(n) = f(n-1) * 2, f(1) = 7

• f(n) = f(n-1) + 14, f(1) = 7

Open Ended

Write the recursive formula for the sequence 10, 60, 360, 2160, ...

Open Ended

Write the recursive formula for the sequence 3, 24, 192, 1536, ...

Open Ended

Write the recursive formula for the sequence -2, 8, -16, 32, ...

Open Ended

Write the first five terms of a sequence if r = 5 and f(1) = 6

Open Ended

Write the first five terms of a sequence if r = -3 and f(1) = 10