CC Algebra 3 Module 1 Sequences & Series Quiz Review 2024

8- 60x +150x²-125x³

Expand: (2-5x)³

x⁴+12x³+54x²+108x+81

Expand: (x+3)⁴

x⁴-12x³+54x²-108x+81

Expand: (x-3)⁴

393,600x²

Find the 5th term of (2x+9)⁶

-1,032,192x⁴

Find the 6th term of: (4x-2)⁹

.0404040404

Find the 99th term of the sequence with the rule: aₙ= (4n/n²)

-9801

Find the 99th term of the sequence with the rule: aₙ=(-1)ⁿn²

At least the first term will be given, and the notation a sub n-1 or a sub n+1 will be used.

How can you tell if a sequence is recursive?

Signs alternate, and the first term is always positive.

How do you handle the signs of a binomial expansion with subtraction (ex. (x-1)⁵)

10

How many terms will be in this expansion? (x-3)⁹

Explicit

Is this rule explicit or recursive? aₙ = ½n-2

2, 4, 6, 8, 10

List the first 5 terms of the sequence with the rule: aₙ = 2n

1, 4, 9, 16, 25

List the first 5 terms of the sequence with the rule: aₙ = n²

3, 5, 7, 9, 11

List the first 5 terms of the sequence with the rule: aₙ= 2n+1

330

Name the 5th term in the 11th row of Pascal's triangle.

1, 7, 21, 35, 35, 21, 7, 1

Name the terms of the 7th row of Pascal's triangle.

2, 6, 12, 20

What are the first 4 terms of the sequence with this rule: aₙ+1=aₙ +2n, a₁=2

2, 5, 8, 11

What are the first 4 terms of the sequence with this rule: aₙ+1=aₙ +3, a₁=2

2, 4, 7, 11

What are the first 4 terms of the sequence with this rule: aₙ+1=aₙ +n, a₁=2

2, -1, -4, -7

What are the first 4 terms of the sequence with this rule: aₙ+1=aₙ - 3, a₁=2

2, 3, 12, 33, 102

What are the first 5 terms of the sequence with this rule: aₙ+1=2(aₙ) +3(aₙ-1), a₁=2, a₂=3

0

What is a₁ of the sequence with this rule? aₙ= 5n-5

-1

What is a₁ of the sequence? -1, -6, -11, -16, -21

-5

What is the common difference (how are you getting the next term) of the sequence with these terms: -1, -6, -11, -16, -21

8

What is the common difference (slope) of the sequence with this rule? aₙ= 8n-5

aₙ=n

What is the sequence rule for the counting numbers?

an=2n

What is the sequence rule for the even numbers?

4,096

What is the sum of the 12th row of Pascal's triangle? (Hint: The sum of any row of the triangle is 2 to the power of the row number).

512

What is the sum of the 9th row of Pascal's triangle? (Hint: The sum of any row of the triangle is 2 to the power of the row number).

4356

What is the sum of the first 11 terms of the sequence with the rule an = n³?

650

What is the sum of the first 12 terms of the sequence with the rule an = n²?

180

What is the sum of the first 20 terms of the sequence with the rule an=9?

483

What is the sum of the first 21 terms of the sequence with the rule an=2n+1?

23936

What is the sum of the first 33 terms of the sequence with this rule? an=2n²-2n

25/12

What is the sum of the first 4 terms of the sequence with the rule an=1/n?

1,640

What is the sum of the first 40 even numbers?

820

What is the sum of the first 40 positive integers?

25

What is the sum of the first 5 terms of the sequence with this rule: aₙ=5

644

What is the sum of the first 7 terms of the sequence with the rule an=n³-n²

2⁰+2¹+2²+2³+2⁴

What is the triangular sum of the first 4 rows of Pascal's triangle?

Sigma means sum

What is this symbol and what does it mean? ∑

1's

What number makes up the two outer rows of Pascal's Triangle?

You would have to find the 98 prior terms first, and that would be very time consuming.

Why would we NOT ask you to find the 99th term of a recursive sequence?

aₙ=n²-1

Write the rule for this sequence: 0, 3, 8, 15, 24...

aₙ=n²+n

Write the rule for this sequence: 2,6,12,20,30