Coordinate Algebra Support
Unit 3C: Arithmetic and Geometric Sequences
Wilson
Geometric Sequences
F.BF.2
Write arithmetic and geometric sequences both recursively and in an explicit formula, use them to model situations, and translate
between the two forms.
Essential Question:
Examples of Geometric Sequences:
1. 1, -4, 16, -64, 256, …
2. 972, -324, 108, -36, …
3. 2, 4, 8, 16, 32, …
2.
3. 2, 4, 8, 16, 32, …
Do you see a pattern?
How do I find the common ratio?
Examples:
1. 1, -4, 16, -64, 256,..
972, -324, 108,-36,…
Recursive Formula:
Example 1:
Write the recursive formula and find the next term for the following sequence: 1, -4, 46, -64, 256, …
Example 2:
Write the recursive formula and find the next term for the following sequence: 972, -324, 108, -36, …
Example 3:
Write the recursive formula and find the next term for the following sequence: 2, 4, 8, 16, 32, …
You Try!
1. 5000, 500, 50, 5, …
2. 3, 12, 48, 192, …
Coordinate Algebra Support
Unit 3C: Arithmetic and Geometric Sequences
Wilson
Geometric Sequences
F.BF.2
Write arithmetic and geometric sequences both recursively and in an explicit formula, use them to model situations, and translate
between the two forms.
Explicit Formula:
Example 1: Use the explicit formula to find the 10th term in the following sequence: 1, -4, 16, -64, 256, …
Example 2: Use the explicit formula to find the 10th term in the following sequence: 972, -324, 108, -36 …
Example 3: Use the explicit formula to find the 20th term in the following sequence:
You Try!
1. Write an explicit rule and find the 8th term. 5000, 500, 50, 5, …
2. Write an explicit rule and find the 12th term. 3, 12, 48, 192, …
Can you write the recursive formula from the explicit formula?
Examples:
1. Write the recursive formula for the following sequence:
( )
2. Write the recursive formula for the following sequence:
You Try!
Write the recursive formula for the following sequences:
1.
2.
Can you write the explicit formula from the recursive formula?
Examples:
1.
2.
You Try!
Write the explicit formula from the given recursive formula.
1.
2.
(
)