Notes 9.3 Geometric Sequences.notebook
April 14, 2015
Notes 9.3: Geometric Sequences
Geometric Sequence ­ a sequence with a constant ratio between consecutive terms
Common Ratio ­ r; the number being multiplied to give the next term in a geometric sequence
Explicit Formula of a Geometric Sequence:
term #
an = a1rn­1
1st term
common ratio
Notes 9.3 Geometric Sequences.notebook
April 14, 2015
Determine if the sequence is arithmetic, geometric, or neither. Identify the common difference or common ratio where appropriate.
1. 3, 6, 12, 48, ...
3. 1, ­2, 4, ­8, 16, ...
2. 3, 6, 9, 12, 15 ...
4. 23, 27, 211, 215, ...
Notes 9.3 Geometric Sequences.notebook
April 14, 2015
Daily Writing Activity!
Describe the similarities and differences between a common difference and a common ratio.
Sample Answer: The common difference, d, and the common ratio, r, are similar in that they are both constant. However, the main difference between them is that the common difference is a number that has been added or subtracted to get to the next term while the common ratio is a number that has been multiplied to get to the next term.
Notes 9.3 Geometric Sequences.notebook
April 14, 2015
Find the nth term of the geometric sequence.
an = a1rn­1
5. Find the 10th term given 4, 12, 36, ...
6. Find a12 given ­16, 8, ­4, 2, ...
7. Find a8 given ­30, 7.5, ­1.875, ...
8. Find the 7th term given 36, 12, 4, ...
Notes 9.3 Geometric Sequences.notebook
April 14, 2015
Write an explicit formula for the geometric sequence.
an = a1rn­1
9. a1 = 1, r = 0.5
11. 10. a1 = 6, r = ­2
12. Notes 9.3 Geometric Sequences.notebook
April 14, 2015
Write an explicit formula for the geometric sequence.
an = a1rn­1
13. a1 = 1, a3 = 4
14. 12.5, __, __, __, 5.12, ... Notes 9.3 Geometric Sequences.notebook
April 14, 2015
When a ball bounces, the heights of consecutive bounces form a geometric sequence.
100cm
70cm
15. What are the heights of the 4th and 5th bounces?
16. Describe the domain and range of this situation.
Notes 9.3 Geometric Sequences.notebook
April 14, 2015
When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of Np­240, a radioactive isotope of Neptunium, initially and after 2 hours.
Hours Elapsed
0
1
Grams of 1244
Np­240
2
3
346
17. What are the amounts left after 1 hour, 3 hours, and 4 hours?
18. Describe the domain and range.
Notes 9.3 Geometric Sequences.notebook
April 14, 2015