Name:______________________________________
Block: ______ Date: ______
3.6 Geometric Sequence
each term is found
by ____________
the previous term
by the same
number
_____________
sequence
3, 6, 12, 24,..
"2n"
•2 •2 •2
The factor between any two consecutive terms in a geometric sequence is called
the ______________ ______________.
State whether the sequence –2, –4, –8, –16, –32, … is geometric. If it is, state the common ratio and
write the next three terms.
–2, –4, –8, –16, –32, _____, _____, _____, …
Notice, that
−4
=
−2
−8
=
−4
−16
−8
=
, and so on.
Write the rule as an algebraic expression: “The previous term n, multiplied by 2” ______________
Sometimes the geometric sequence looks like the term is divided, but it’s really multiplying a fraction.
State whether the sequence is geometric. If it is, find the values of the following:
81, 27, 9, 3, 1,
1
,…
3
Common ratio: _______
1, –5, 25, –125, …
–32, –8, –2, …
Common ratio: _______
Common ratio: _______
Next three terms: ____, ____, ____ Next three terms: ____, ____, ____ Next three terms: ____, ____, ____
Ninth term: __________
Eighth term: __________
Seventh term: __________
Rule: __________
Rule: __________
Rule: __________
If the signs of all terms are the same (all positive OR all negative), then the common ratio is _____________.
If the sign change for every next term, then the common ratio is ___________________,.
State if each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic or geometric, fill in the table
and describe the relationship (write the rule) between two consecutive terms in the sequence.
Sequence
arithmetic,
geometric, or neither
Common
difference/ratio
Next three terms
Relationship
0, 3, 6, 9, 12, . . .
48, 24, 12, 6, 3, . . .
6, 11, 16, 21, 26, . . .
0, 1, 3, 6, 10, . . .
1
9
1
, 3 , 1, 3, 9, . . .
30, 26, 22, 18, 14, . . .
–3, –6, –12, –24, . . .
–4, 4, –4, 4, –4, . . .
–5, 10, –20, 40, . . .
1, 2, 1, 2, 1, . . .
448, 224, 112, 56, . . .
1. Write a sequence for the perimeters of the rectangles.
Is the sequence arithmetic or geometric? ________
Common difference/ratio: _______
Next three terms: ______, ______, ______
Rule: ________
2. Write a sequence for the areas of the rectangles: _______, _______, _______, _______
Is the sequence arithmetic or geometric? ________
Common difference/ratio: _______
Next three terms: ______, ______, ______
Rule: ________
3. Write an arithmetic sequence in which the common difference is –5. ____________________________________
HOMEWORK 3.5
Sequence
arithmetic,
geometric, or neither
Common
difference/ratio
Next three terms
Rule
35, 28, 21, 14…
1, 3, 9, 27…
2, –4, 8, –16…
121, 1221, 12221 …
1
4
1
, − 2 , 1, –2, 4, . . .
–8, –6, –4, –2…
2, 6, 24, 120…
–2, –6, –18, –54 …
8) What is the 6th term of the arithmetic sequence:
29 , 21 , 13 , 5 ,
_______
9) Find the missing terms in the sequence 26, 33, 40, ___, 54, 61, ___, …
13) Create three sequences. One sequence must be arithmetic, one sequence must be geometric, and one
sequence must be neither. Then describe the relationship (write the expression using n) between two
consecutive terms in each of your arithmetic and geometric sequences.
Arithmetic: ________________________________________ ______________
Geometric: ________________________________________ ______________
Neither:
________________________________________
Look for a pattern. Then use the pattern to solve each problem.
There were 256 people at a fundraiser. When the event was over, half of the people who remained left every 5 minutes.
How long after the event ended did the last person leave?
A knitting shop is having a huge yarn sale. One skein sells for $1.00, 2 skeins sell for $1.50, and 3 skeins sell for $2.00. If
this pattern continues, how many skeins of yarn can you buy for $5.00?
The football cheerleaders will arrange themselves in rows to form a pattern on the football field at halftime. In the first
five rows there are 12, 10, 11, 9, and 10 girls in each row. They will form a total of twelve rows. If the pattern continues,
how many girls will be in the back row?
Find the perimeters of the next two figures in the pattern. The length of
each side of each small square is 3 feet.
A hot tub holds 630 gallons of water when it is full. A hose fills the tub at a
rate of 6 gallons every five minutes. How long will it take to fill the hot tub?
Jordan saved $1 the first
week, $2 the second week, $4 the third
week, and $8 the fourth week. If this
pattern continues, how much will she
save the eighth week?