1. (−10𝑥)
0
12𝑛8
4.
4𝑛8
Warm Up 1 – 20 - 15
2
4
2𝑥
2.
𝑦
3.
5
𝑐 ∙𝑐∙𝑐
1
3
5
2
4
1
2
5. 4
6. 64 + 9
radical form:
answer:
radical form:
answer:
7.
4
8
16𝑛
8. Is this sequence Geometric, if so what is the
Common Ratio?
2, -6, 18, -54, …
9. Write the Function Rule and find the 9th term
2, 6, 18, 54 …
Formula
10. Find the next three terms of the sequence:
-5, 10, -20, ____ , ____ , ____ , . . .
1. (−55)
0
18𝑚3
4.
6𝑚3
Warm Up 1 – 16 - 15
2
4
11𝑥
2.
3.
𝑦
2
3
4
𝑏 ∙𝑏∙𝑏
1
3
2
1
2
5. 64
6. 27 + 81
radical form:
answer:
radical form:
answer:
7.
4
8
16𝑛
8. Is this sequence Geometric, if so what is the
Common Ratio?
2, 8, 32, 128, …
9. Write the Function Rule and find the 9th term
1, 6, 36, …
Function Rule
10. Find the next three terms of the sequence:
32, -16, 8, -4, ____ , ____ , ____ , . . .
1. 11𝑦
4.
−4
4
3
8
Warm Up 1 – 15 - 15
3
3
5𝑛
2.
𝑝
10𝑧 4
5.
5𝑧 4
6
𝑟 ∙𝑟
3.
−7
1
3
6. 125
radical form:
answer:
Write the Function Rule and find the 11th term
7.
4
12
81𝑦
8. Geometric sequences:
3, 12, 48, …
1. 4−4
4
3
4. 27
7.
4
16𝑘 8 𝑚4
Warm Up 1 – 14 - 15
2. 13𝑥 −4 2
5.
8.
𝑧2
9 12
6. 125𝑥 𝑦
𝑧8
3
3. 𝑛−6 ∙ 𝑛4 ∙ 𝑥 5
8𝑥 6 𝑧15
9.
8
16
81𝑛 𝑝
1
4
1
3
UNIT 6 DAY 3: GEOMETRIC
SEQUENCES
Essential Questions: What is a geometric sequence?
How can you find any term in a geometric sequence?
VOCABULARY
•
Geometric Sequence: A sequence that uses multiplication
•
Common Ratio (r): the multiplier
•
Function Rule for a Geometric Sequence: an = a1rn-1
•
a1: first term
•
r: common ratio
•
n: nth term (wanted term)
GEOMETRIC SEQUENCES AS FUNCTIONS
Geometric sequences can be thought of as functions. The
term number, or position in the sequence, is the input, and
the term itself is the output.
1
2
3
3 6 12
a1 a2 a3
4
Position
24
a4
Term
What is the common ratio?
2
48
What would the 5th term be?
EXAMPLE 1: FIND THE COMMON RATIO AND THE
NEXT THREE TERMS OF EACH SEQUENCE.
1, 3, 9, 27, …
-16, 4, -1, 1/4, …
r=3
r = - .25
81, 243, 729
-1/16, 1/64, -1/256
5, -10, 20, -40, …
512, 384, 288, …
r = -2
r = .75
80, -160, 320
216, 162, 121.5
FINDING THE FUNCTION RULE
an = a1rn-1
EXAMPLE 2: FIND THE FUNCTION RULE FOR THE SEQUENCE
WITH THE INFORMATION GIVEN. THEN FIND THE WANTED
TERM.
he first term is 128 and the common ratio is .5. Find the 10th term
an = 128(.5)n-1
Function Rule
a10 = 128(.5)10-1
a10 = 128(.5)9
a10 = 128(.001953125)
a10 = 0.25
EXAMPLE 3: FIND THE FUNCTION RULE FOR THE SEQUENCE
WITH THE INFORMATION GIVEN. THEN FIND THE WANTED
TERM.
a1 = 8 and r = 3. Find the 5th term.
an = 8(3)n-1
a5 = 8(3)5-1
a5 = 8(3)4
a5 = 8(81)
a5 = 648
Function Rule
EXAMPLE 4: FIND THE FUNCTION RULE FOR THE SEQUENCE
WITH THE INFORMATION GIVEN. THEN FIND THE WANTED
TERM.
What is the 13th term of the sequence 8, -16, 32, -64, ….?
a1 = 8
r = -2
an = 8(-2)n-1
a13 = 8(-2)13-1
a13 = 8(-2)12
a13 = 8(4096)
a13 = 32,768
Function Rule
EXAMPLE 5: A BUNGEE JUMPER JUMPS FROM A BRIDGE. THE
FIRST BOUNCE IS 200 FEET, THE SECOND BOUNCE IS 80 FEET,
AND THE THIRD BOUNCE IS 32 FEET. WHAT IS THE HEIGHT OF
THE 5TH BOUNCE?
200 , 80 , 32, …
a1 = 200
r = .4
an = 200(.4)n-1
a5 = 200(.4)5-1
a5 = 200(.4)4
a5 = 200(.0256)
a5 = 5.12 feet
Function Rule
SUMMARY
Essential Questions: What is a geometric sequence?
How can you find any term in a geometric sequence?
Take 1 minute to write 2 sentences answering the essential
questions.