1. How does the geometric sequence differ from the arithmetic sequence?
Geometric Sequences
How does the geometric sequence differ from the arithmetic sequence?

2. QUICK REVIEW
In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.
Unlike in an arithmetic sequence, the difference between consecutive terms varies.
We look for multiplication to identify geometric sequences.

3. Determine if the sequence is geometric
Determine if the sequence is geometric. If so, identify the common ratio
1, -6, 36, -216
yes. Common ratio = -6
2, 4, 6, 8
no. No common ratio

4. Formula for Geometric Sequence
an = a1 • r n-1
Where:
an is the nth term in the sequence
a1 is the first term
n is the number of the term
r is the common ratio

5. Write the next three terms given: 11,33,99,297 . . .
Geometric Sequences
Write the next three terms given: ,33,99,
Find the common ratio between the values.
Common ratio = 3
So multiply 297 by 3 three times and you will get…
891, 2673, 8019.

6. Given the sequence of 11,33,99,297 . . .Find the 19th term
Geometric Sequences
Given the sequence of ,33,99, Find the 19th term
an = a1 • r n-1
Use the first term and find the common ratio
Common ratio = 3
a19 = 11 (3) (19-1)
Plug in known values
a19 = 11(3)18 =4,261,626,379
Simplify

7. Find the 10th term in the sequence of 1, -6, 36, -216 . . .
Try This One!
Find the 10th term in the sequence of , -6, 36,
an = a1 • r n-1
Start with the geometric sequence formula
Find the common ratio between the values.
Common ratio = -6
a10 = 1 (-6) (10-1)
Plug in known values
a10 = 1(-6)9 = -10,077,696
Simplify

8. Geometric Sequences (1) 8, 4, 2, 1, …………….. (2) 11, 22, 44, 88, ……………
(3) 1, 1/3, 1/9, 1/27,……………..
(4) 5, -15, 45, -135,………………
Find the common ratio, the next three terms and the 12th term for each.

9. ANSWERS
(1) 8, 4, 2, 1, …………….. r = 0.5, ….0.5, 0.25, 0.125,…
(2) 11, 22, 44, 88, ……………r = 2, 176, 352, 704,…..22,528
(3) 1, 1/3, 1/9, 1/27,………r = 1/3, 1/81, 1/243, 1/729,……
(4) 5, -15, 45, -135,………………r = -3, 405, -1215, 3645, ……

10. WORD PROBLEMS
A mine worker discovers an ore sample containing 500 mg of radioactive material.  It is discovered that the radioactive material has a half life of 1 day.  Find the amount of radioactive material in the sample at the after the 7th day.
Answer is mg  

11. WORD PROBLEMS
You visit the Grand Canyon and drop a penny off the edge of a cliff.  The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on. What is the total distance the object will fall in 6 seconds?
Answer is 576