ALGEBRA 1E
Unit 8
8-1
Arithmetic Sequences
*193/1–4, 7(do not graph), 8–17, 18 and 20(do not graph, but also find the 10th term)
8-2
Geometric Sequences
*441/ 1 – 12
193/19 and 21 (do not graph, but also find 10th term)
8-3
Review of Explicit (General) Form of Arithmetic and Geometric Sequences
WS 7-3/ ALL
441/14 – 28 Even
206/ 39 – 43
8-4
Recursive Form of a Sequence
*448/1 – 9
441/15 – 27 Odd
8-5
Recursive Form of a Sequence (Continued)
448/ 11-25 Odd
450/ 36-40
8-6
Arithmetic Sequences as Linear Functions
*193/ 5, 6, 7, 18, 20, 22, 23
448/10, 12, 16, 24
*WS 7–6/1-6
8-7
Geometric Sequences as Exponential Functions
*441–442/ 13, 30, 31, 33, 35
448/14, 18, 20, 26
*WS 7–6/7-12
8-8
More Verbal Problems/Direct Variation
*201–202/11, 12, 13, 28
*194/ 31 (Graph also)
*207/15–19
8-9
Review Day
8-10
Unit 8 Test
ALGEBRA 1E
NAME: _______________________________________
WORKSHEET 8 – 3: GENERAL FORM OF A SEQUENCE
Write the first four terms of the sequence specified by the general form of the sequence.
1.
ak  2k  3
2.
ak  3k
3.
an  4n 2
4.
an  2n  1
Write each sequence in general formula (in terms of n).
5.
3, 4, 5, 6,…
7.
4, 8, 12, 16,…
8. 2, 4, 8, 16,…
9.
6, 16, 26, 36,…
10. –5, –10, –15, –20,…
ALGEBRA 1E
6.
2, 4, 8, 16,…
NAME: _______________________________________
WORKSHEET 8 – 6: GRAPHS AS SEQUENCES
Define the following linear functions as arithmetic sequences starting at x = 1 and give the general
form of the sequence.
y
y
y
3.
2.
1.
x
x
y
y
y
4.
x
6.
5.
x
x
x
Define the following exponential functions as geometric sequences starting at x = 1 and give the
general form of the sequence.
y
y
y
9.
8.
7.
x
x
y
y
y
10.
11.
x
x
12.
x
x
ALGEBRA 1E
NAME: _____________________________
UNIT 8 REVIEW SHEET
1.
Given the sequence –8, –11, –14, –17,…
a) Write an equation for the nth term of the arithmetic sequence
b) Using the formula from part a, find the 16th term of the sequence
c) Using the formula from part a, which term of the sequence is –122?
2.
Determine if the following sequences are arithmetic, geometric or neither and state the
common difference or common ratio.
a. 2, 4, 7, 11,…
3.
b. 2, 4, 8, 16, ,… c. 15, 18, 21, 24,…
Given the sequence 24, 12, 6, 3,…
a) Write an equation for the nth term of the geometric sequence
b) Find the 8th term of the sequence
4.
Write the first four terms of the sequence specified by the general form of the sequence
an  7n  8
5.
Write each sequence in general formula (in terms of n).
a. 15, 30, 45, 60,…
6.
b. –3, –9, –27, –81,…
Write the first five terms of the sequence specified in which
a1  5, and an  3an1  2 , n  2
7.
a) Determine if the following sequence is arithmetic, geometric or neither and determine
the common difference or common ratio.
6, 20, 34, 48,…
b) Write the recursive formula for the sequence.
8.
Jake was playing a Marvel Avenger’s board game in which a player is rewarded each time
they spin. After the first spin, Fred had 10 MP (Marvel Points), after the second spin he had
30 MP, and after the third spin he had 50 MP.
(a) Write a function (using arithmetic sequences) that represents this board game.
(b) Graph the function and determine the domain
9.
Write the first five terms of the sequence specified in which
a1  1, and an  (2)an1  5 , if n  2 .
10.
If y varies directly with x and y = 84 when x = 30, find y when x = 42.
11.
a. In the table below, tell whether one variable varies directly as the other (Yes or No).
b. If it does, express the relationship as a formula.
n
2
4
6
8
q
5
10
15
20
a __________________
b __________________
12.
Mr. Paschke dropped a super ball from the top of the school (a height of 24 feet). Each time
the ball bounces back to 70% of the height that it fell.
(a) Write a function (using geometric sequences) that represents this situation.
(b) Graph the function and determine the domain
13.
Define the following linear functions as arithmetic sequences starting at x = 1 and give the
y
general form of the sequence.
x
14.
Define the following exponential functions as geometric sequences starting at x = 1 and give
y
the general form of the sequence.
x
15.
Solve the following quadratic equation using the quadratic formula. Round you answers to
the nearest hundredth.
2 x 2  3x  7
16.
Solve the following quadratic equation using the completing the square method. Round you
answers to the nearest hundredth.
2 x 2  3x  7
MIDTERM CORRECTIONS: THERE WILL BE 10 QUESTIONS FROM THE PART 1 OF YOUR MIDTERM
EXAM. MAKE SURE YOU HAVE LOOKED THEM OVER!!!!
ALGEBRA 1E
UNIT 8 REVIEW ANSWERS
1.an = –8 + (n – 1)d or an = –3n – 5
2. b. Geometric, r = 2
9. –5, 7, –9, 23, –41
2
5
q or q  n
5
2
3
16
10.117.6
14. –1, –3, –9; an = –(3)n –1 15 and 16. –2.77 and 1.27
12b.height
27
80
24
70
21
60
18
50
15
spin
1 2 3 4 5 6 7 8 9
D = {1, 2, 3, …}
12
9
20
6
10
3
bounce
1 2 3 4 5 6 7 8 9
D = {1, 2, 3, …}
ALGEBRA 1E
UNIT 7 REVIEW ANSWERS
1.an = –8 + (n – 1)d or an = –3n – 5
2. b. Geometric, r = 2
b. a8 
12. a. a(n) = 24(.70)n –1 b. GRAPH BELOW
90
30
n 1
b. an = –(3)n –1 6. –5, –13, –37, –109, –325
13. 4, 2, 0, –2; an = –2n + 6
8b.cubes
40
2. a. Neither
b. a1  6, and an  an1  14 , n  2 8. a. a(n)  10  (n  1)(20) or a(n)  20n  10
8b. GRAPH BELOW
11. a. Yes b. n 
c. 39th
1
3. a. an  24  
2
c. Arithmetic, d = 3
4. –1, 6, 13, 20 5. a. an = 15n
7. Arithmetic, d = 14
b. a16 = –53
b. a16 = –53
c. Arithmetic, d = 3
c. 39th
2. a. Neither
1
3. a. an  24  
2
n 1
b. a8 
3
16
4. –1, 6, 13, 20 5. a. an = 15n
7. Arithmetic, d = 14
b. a1  6, and an  an1  14 , n  2 8. a. a(n)  10  (n  1)(20) or a(n)  20n  10
8b. GRAPH BELOW
11. a. Yes b. n 
b. an = –(3)n –1 6. –5, –13, –37, –109, –325
9. –5, 7, –9, 23, –41
2
5
q or q  n
5
2
12. a. a(n) = 24(.70)n –1 b. GRAPH BELOW
13. 4, 2, 0, –2; an = –2n + 6
8b.cubes
14. –1, –3, –9; an = –(3)n –1 15 and 16. –2.77 and 1.27
12b.height
90
27
80
24
70
21
60
18
50
15
40
30
spin
1 2 3 4 5 6 7 8 9
D = {1, 2, 3, …}
10.117.6
12
9
20
6
10
3
bounce
1 2 3 4 5 6 7 8 9
D = {1, 2, 3, …}