Algebra 1 Sequences and CPM Review
Name___________________Period______
Determine whether the sequence is arithmetic, geometric, or neither.
2. 80, 40,  20, 10,
1. 1, 3, 6, 10,
3. 2 , 1 ,  1 ,  5 ,
3 6 3 6
4.
1 , 1 , 1 , 1,
64 32 16 8
5. State whether the sequence is defied explicitly or recursively. Then determine if the sequence is arithmetic, geometric,
or neither. Write the first six terms of the sequence.
a. an  102
n 1
b. a1  24, an 1   1 an 1
2
Write a recursive rule for the sequence.
6.
Position, n
1
2
3
Term, an
27
9
3
7.
Position, n
1
2
3
4
Term, an
2
3
5
9
8.The first two terms of a sequence are a1  2 and a2  1. Let a3 be the third term when the sequence is arithmetic
and let b3 be the third term when the sequence is geometric. Find 2a3  b3.
9. Write an explicit and recursive formula for the following sequences.
10. Given the recursive formula, write the explicit formula for the sequence.
a.
b.
c.
d.
11. Given the explicit formula, write the recursive formula for the sequence.
a.
b.
c.
d.
12. Multiply the following expressions.
a.
b.
c.
d.
13. The tiles shown at right have the given dimensions. Using 1, g, g2, h, h2, and gh write the value of the figure below
algebraically.
14. Write an algebraic equation for each figure below to express the relationship, "Area as a product equals area as a
sum."
15.
2-70. Examine the shape made with algebra tiles at right.
a. Write an expression that represents the perimeter of the shape. Then evaluate your
expression for x= 6 and y = 10 units.
a. Write an expression that represents the area of the shape. What is the area if x = 6 and y = 10
units?
16. Use a generic rectangle to multiply the following.
a. 3x  6
2
c.
(6 x 2  x  9)(7 x  1)

b.  7 x 8x  3x
2
d. 6w  85w  9

1
1
e. (4𝑥 − 5) (15𝑥 − 8)
17. Fill in each blank to make the statement true.
18. Write the area of the rectangle below as a product and as a sum. The following is a key for the tiles below.
Sequences and CPM review answers
1.
2.
3.
4.
5.
Neither
Geometric
Arithmetic
Geometric
a.
b.
6. a.
7.
8.
9. a. 𝑎𝑛 = -2n -2
b. 𝑎𝑛 = -13n +97
10.
𝑎𝑛 = 6n -6
b. 𝑎𝑛 = -4 𝑎𝑛 = 𝑎𝑛−1 -2
b. 𝑎𝑛 = 84 𝑎𝑛 = 𝑎𝑛−1 -13
b 𝑎𝑛 = -4n +12
11a 𝑎𝑛 =2 𝑎𝑛 = 𝑎𝑛−1 +3
c. 𝑎𝑛 = -3(−3)𝑛−1
b. 𝑎𝑛 = -3 𝑎𝑛 = 𝑎𝑛−1 -5
d. 𝑎𝑛 = 2(5)𝑛−1
1
c. 𝑎𝑛 = 1 𝑎𝑛 = 3𝑎𝑛−1 d. 𝑎𝑛 = 2 𝑎𝑛 = 4 𝑎𝑛−1
12. a: 2x2 + 7x + 3, b: x2 – x – 30, c: 4m + 32, d: x2 + 6x + 9
13. 4g2 + 2h2 + 4g + 5h + 2gh + 4
14.
15. a. 2x + 4y +2 ;54
b. 𝑦 2 + 2x +1 ; 113
1
1
16. a. 9𝑥 2 + 36x + 36 b. -56𝒙3 + 21𝑥 2 c. 42𝒙3 + 𝒙𝟐 -64x + 9 d. 30 𝑤 𝟐 -94w + 72 e. 60𝒙𝟐 - 32x + 40
17. a: x2 + 4x + 5, b: 2x2 + 1, c: 2x + 1
18. (2x +1)(x+6) = 2𝒙𝟐 + 13X + 6