1. Warm Up
Find the next 3 terms in the following sequence and describe the pattern
1) 3, 7, 11,15, 19, _______, _______, _______ Pattern:_________________
2) -3, -1, 1,3, 5, _______, _______, _______ Pattern:_________________
3) 2, 6, 18, 54, 162, _______, _______, _______ Pattern:_________________

2. Today’s Lesson: Geometric Sequences
March 3, 2014

3. Recall………
Problems number 1 and 2 are different from number 3 because the terms increase by adding a certain amount.
#1 and #2 are called arithmetic sequences
#3 increased by a factor of 3. Arithmetic sequences did not increase by being multiplied by a number.
In fact #3 is actually a geometric sequence.

4. Geometric Sequences
Geometric Sequence: a sequence in which each term after the first is found by multiplying the previous term by a constant value called the common ratio.

5. Think about it…
What if your pay check started at $100 a week and doubled every week. What would your salary be after four weeks?

6. Geometric Sequence Starting $100. After one week - $200
After two weeks - $400
After three weeks - $800
After four weeks - $1600.
These values form a geometric sequence.

7. Still Don’t Get It?
Find the first five terms of the geometric sequence with a1 = -3 and common ratio (r) of 5.
ANSWER: -3, -15, -75, -375, -1875

8. Geometric Sequence
Find the common ratio of the sequence 2, -4, 8, -16, 32, …
To find the common ratio, divide any term by the previous term.
8 ÷ -4 = -2
r = -2

9. Geometric Sequence Let’s figure out the formula(s)…
Recursive form: NEXT = ____ NOW
OR an=an-1•r
Explicit form: =(y = abx )

10. Salary Example Starting $100. After one week - $200
After two weeks - $400
After three weeks - $800
After four weeks - $1600.
Recursive form: NEXT = ____ NOW
Explicit form: an = a1•rn-1

11. Example
an = a1•rn-1
Find the 10th term of the geometric sequence with a1 = 2000 and a common ratio of 1/2.

12. Example
an = a1•rn-1
Find the next two terms in the sequence -64, -16,

13. Classwork

14. Classwork

15. Classwork

16. Geometric Sequences Worksheet: Evens Only
Homework
Geometric Sequences Worksheet: Evens Only