Download Algebra 1 Sequences (replacing sections 4.6 and 11.1) Name: Part

Algebra 1 Sequences (replacing sections 4.6 and 11.1)
Name: _______________________
Part A
A sequence is a list of numbers that may form a pattern. Each number in a sequence is called
a term.
Position
Term
Term’s label
1
2
a1
2
4
a2
3
6
a3
4
8
a4
…
…
n
an
Try to best complete each sequence.
3, 6, 9, _____, _____, _____, _____
21, 16, 11, _____, _____, _____, _____
10, 9.8, 9.6, _____, _____, _____, _____
3, 9, 27, _____, _____, _____, _____
32, 16, 8, _____, _____, _____, _____
3, 6, 12, _____, _____, _____, _____
81, 54, 36, _____, _____, _____
3, 7, 11, _____, _____, _____, _____
2, 5, 11, 22, _____, _____, _____
2, 3, 6, 15, _____, _____, _____
1, 4, 9, 16, _____, _____, _____, _____, _____, _____, _____, _____
1, 1, 3, 5, 9, 17, _____, _____, _____
2, 1, 3, 0, 4, -1, 5, _____, _____, _____
9, 10, 24, 20, 24, 24, 18, 27, 13, 3, 17, 38, _____
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Part B
When the terms of a sequence differ by the same nonzero number d, the sequence is an
arithmetic sequence and d is the common difference. (when you add or subtract something
to/from each term)
Complete each arithmetic sequence. Find the common difference d. If able, find the indicated
term; if unable, come back to that part later.
5, 7, 9, _____, _____, _____
d = _____; a50 = _____
2, 5, 8, _____, _____, _____
d = _____; a50 = _____
5, -7, -19, _____, _____, _____
d = _____; a50 = _____
1/2 , 5/8, 3/4, _____, _____, _____
d = _____; a50 = _____
Part C
In a geometric sequence, the ratio of successive terms is the same number r, called the
common ratio. (when you multiply—or divide—by something for each term)
Complete each geometric sequence. Find the common ratio r. If able, find the indicated term; if
unable, come back to that part later.
2, 6, 18, _____, _____, _____
r = _____; a10 = __________
2, 4, 8, _____, _____, _____
r = _____; a10 = __________
0.1, -1, 10, _____, ______, _______
r = _____; a10 = __________
176, 88, 44, _____, _____, _____
r = _____; a7 = _____
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Part D
1, 1, 2, 3, 5, 8, 13, _____, _____, _____, _____, _____, _____, _____, _____
Can you find the pattern?
This sequence is a famous sequence whose numbers occur frequently in nature; it is called the
Fibonacci sequence. After the first two terms, each term is the sum of the previous two terms.
Complete the sequence.
Is the Fibonacci sequence arithmetic? _____ Is it geometric? _____
Notice that the 3rd term is divisible by two. Is the 6th term divisible by two? ____ …the 9th? ____
What conclusion can you draw about every third term?
Why is this true?
What do you notice about every 4th term?
What do you notice about every fifth term?
Triangular Numbers Complete the table.
1
3
6
10
Perfect Squares Complete the top row of the table. You may also do the bottom row if it helps.
1
4
9
16
Perfect Cubes: Complete the sequence. 1, 8, 27, _____, _____, _____, _____
1x1x1
2x2x2
3x3x3
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Part E
Warm-Up: A ball is dropped from a height of 2 meters and allowed to bounce. What happens
to the height of each bounce?
Would the bounce height form a sequence?
If so, what type of sequence do you expect it to form?
Record your predictions for a ball drop. 2m, ______, ______, ______, ______, ______
*Classify each sequence in Part A as arithmetic, geometric, or neither. Record the common
difference, d, for each arithmetic sequence. Record the common ratio, r, for each geometric
sequence.
Part F
Ball Bounce Activity
Ball:
Initial Height
1st Bounce
2nd Bounce
3rd Bounce
4th Bounce
5th Bounce
3rd Bounce
4th Bounce
5th Bounce
…3rd object
…4th object
…5th object
What type of sequence does it appear to form?
Ball:
Initial Height
1st Bounce
2nd Bounce
What type of sequence does it appear to form?
Part G
Activity
Object:
Initial Mass
Mass after one
object is removed
…2nd object
What type of sequence does it appear to form?
Without actually weighing them, estimate the mass after 10 objects have been removed.
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Part H
Finding a term of an arithmetic sequence:
Finding the nth term of an arithmetic sequence:
Finding a term of an geometric sequence:
Finding the nth term of an geometric sequence:
*Complete Part B and Part C if you have not already done so.
Find the 100th term of an arithmetic sequence if the first term is -10 and the common difference
is 2.
Find the first term of an arithmetic sequence for which the 51st term is 444 and the common
difference is 4.
Find the first term of an arithmetic sequence for which the 20th term is 126 and the 19th term is
123.
Find the 10th term in a geometric sequence where the first term is 1 and the common ratio is 2.
Find the first term in a geometric sequence in which the 5th term is 8000 and the common ratio
is 0.1.
If a6 = 729 and a5 = 243, find the 1st term of the geometric sequence.
A box of frozen ¼ pound hamburgers has a mass of 27 pounds when there are 100 hamburger
patties in the box. Consider the sequence: a100 = 27, a99 = 26.75, a98 = 26.5, a97 = 26.25, a96 =
26, etc.
Calculate the mass when 90 hamburgers are in the box.
If the mass is 10 pounds, how many hamburgers remain?
Calculate the mass of the empty box.
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Part I
In the NCAA men’s basketball tournament, 64 teams compete in round 1. Only the winners
advance, so there are 32 teams competing in round 2. This continues until all but one team
remains.
How many teams compete in round 3?
How many teams compete in round 5?
After which round, is the champion determined?
Adaptation of #46 on p.795 (you may refer to that page if you wish)
The frequency of a musical note, measured in hertz (Hz), is called its pitch. The pitches of the A
keys on a piano form a geometric sequence.
A1 = 55 Hz; A2 = 110 Hz; A3 = 220 Hz; A4 = 440 Hz
What is the frequency of A7?
Answer #33 on p.794.
a)
b)
Complete #41 on p.794.
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Part J
Sequences using MS EXCEL
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