Ch. 4 Pretest
Sequences
Name ______________________________
Period _________
Show all of your work on a separate piece of paper!
For each pattern, A) Describe the pattern,
B) Draw the next two figures and
C) Write a numeric sequence to represent what is happening.
(1)
(2)
(3)
(4)
For each problem scenario, A) Write a numeric sequence showing the first 7 terms,
B) Determine if it is Arithmetic or Geometric
C) Determine the common ratio or difference
D) Determine the 10th term of the sequence
(5) The school cafeteria begins the day with a supply of 1000 chicken nuggets. Each student that passes
through the lunch line is given 5 chicken nuggets. Write a numeric sequence to represent the number of chicken
nuggets left for the first seven students.
(6) Kyle is collecting canned goods for a food drive. On the first day he collects 1 can. On the second day he
collects 2 cans. On the third day he collects 4 cans. On each successive day he collects twice as many cans as he
collected the day before. Write a numeric sequence to show the total number of cans for the first seven days.
(7) Leonardo uses 3 cups of flour in each cake he bakes. He starts the day with 50 cups of flour. Write a
numeric sequence to represent the amount of flour remaining after each of the first 7 cakes Leonardo bakes.
(8) For her 15th birthday, Leslie’s grandparents give her a set of 100 stamps. For each birthday after that, they
give her a set of 20 stamps to add to her stamp collection. Write a numeric sequence consisting of 7 terms to
represent the number of stamps in Leslie’s collection after each of her birthdays starting with her 15th birthday.
Determine the common difference for each arithmetic sequence.
1 2
4
(9) 10, 3, −4, −11, …
(10) , , 1, , …
3
(11) 170, 240, 310, 380, …
3
3
(12) −28, −13, 2, 17, …
Determine the common ratio for each geometric sequence.
9
9
(13) 2, −8, 32, −128, …
(14) 45, 9, , , …
5
(15) 270, 90, 30, 10, …
25
(16) −5, −10, −20, −40, …
Determine whether each given sequence is arithmetic, geometric, or neither. Then write
the next 3 terms of the sequence.
(17) 4, 8, 12, 16, __ , __ , __
(18) 1, 1, 2, 2, 3, 3, 4, __ , __ , __
(19) 17, 34, 68, 136, __ , __ , __
(20) −15, −18, −21, −24, __ , __ , __
(21) 1, 1, 2, 3, 5, 8, __ , __ , __
(22) −243, −81, −27, −9, __ , __ , __
For each sequence, FIRST write 1) the explicit formula for the sequence and then
2) Determine the unknown term USING your formula.
(23) 3, 7, 11, 15, … , 𝒂𝟒𝟎 , …
(24) −5, −8, −11, −14, … , 𝒂𝟑𝟎 , …
(25) 8, 16, 24, 32, … , 𝒂𝟑𝟓 , …
(26) 12, 6, 0, −6, … , 𝒂𝟓𝟎 , …
(27) 2, 6, 18, 54, … , 𝒈𝟐𝟎 , …
(28) 5, 20, 80, 320, … , 𝒈𝟏𝟖 , …
(29) 500, 100, 20, 4, … , 𝒈𝟏𝟎 , …
(30) 6, 24, 96, 384, … , 𝒈𝟐𝟓 , …
Complete the table and then graph.
1 𝑛−1
35) 𝑎𝑛 = 8 − 2(𝑛 − 1)
Term #
(𝑛)
1
2
3
4
5
6
36) 𝑔𝑛 = 24 ∙ ( )
2
Term Value
( 𝑎𝑛 )
Term Value
( 𝑔𝑛 )
38) 𝑔𝑛 = −2 ∙ (4)𝑛−1
37) 𝑎𝑛 = −9 + 6(𝑛 − 1)
Term #
(𝑛)
1
2
3
4
5
6
Term #
(𝑛)
1
2
3
4
5
6
Term Value
( 𝑎𝑛 )
Term #
(𝑛)
1
2
3
4
5
6
Term Value
( 𝑔𝑛 )
REVIEW:
Simplify.
38) 5 − 2(𝑥 − 4) − (𝑥 − 7)
39) 𝑤 − 3(𝑤 + 1) − 𝑤(𝑤 + 6)
Solve for x.
40) 2 − 4(𝑥 + 1) = 5𝑥 + 1
41)
Write in slope-intercept form.
42) 2𝑥 + 3𝑦 = 9
43) 5𝑥 − 4𝑦 = −16
Write in standard form.
44) 𝑦 = 5𝑥 + 3
45) 𝑦 = − 𝑥 − 4
Simplify the following expressions.
46)
𝟑𝟒
(−𝟐)𝟓
( )𝟑
𝟓𝟎
(−𝟐)−𝟑
(−𝟏𝟐)𝟎
𝟖𝟏
2
3
𝑥−5=8
3
4
𝟏
(− )𝟎
𝟐
𝟏
𝟓
47) What kind of function is an arithmetic sequence?
What kind of function is a geometric sequence?
𝟒−𝟐