Deck 10: Sequences and Series

Question 1

Evaluate the binomial coefficient

A) 6
B) 720
C) 0.55
D) 30

Answer 1

6

Question 2

Evaluate the binomial coefficient

A) 5,040
B) 210
C) 40
D) 52.50

Answer 2

210

Question 3

Evaluate the binomial coefficient

A) 3,876
B) 300
C) 15,504
D) 232,560

Answer 3

15,504

Question 4

Evaluate the binomial coefficient

A) 1,367,206.5
B) 2,515,659,960
C) 1,880
D) 62,891,499

Question 5

Evaluate the binomial coefficient

A) 1,037,836,800
B) 286
C) 130
D) 2,860

Question 6

Expand (x - 2)⁵ using the binomial theorem.

A) x⁵ - 10x⁴ + 40x³ - 80x² + 80x - 32
B) x⁵ + 10x⁴ + 40x³ + 80x² + 80x + 32
C) x⁵ - 10x⁴ - 40x³ - 80x² - 80x - 32
D) -x⁵ + 10x⁴ - 40x³ + 80x² - 80x + 32

Question 7

Expand (4x + 5)³ using the binomial theorem.

A) 125x³ + 100x² + 80x + 64
B) 64x³ + 80x² + 100x + 125
C) 125x³ + 300x² + 240x + 64
D) 64x³ + 240x² + 300x + 125

Question 8

Expand using the binomial theorem.

A) 81x⁴ + 108(x³y) + 54(x²y²) + 12(xy³) + 1y⁴
B) 81x⁴ + 108(x³/y) + 54(x²/y²) + 12(x/y³) + 1/y⁴
C) x⁴ + 12(x³/y) + 54(x²/y²) + 108(x/y³) + 12/y⁴
D) 81x⁴ + 27(x³/y) + 9(x²/y²) + 3(x/y³) + 1/y⁴

Question 9

Expand (3x - y)⁴ using Pascal's Triangle.

A) -81x⁴ + 108x³y - 54x²y² + 12xy³ - y⁴
B) 81x⁴ - 108x³y + 54x²y² - 12xy³ + y⁴
C) 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴
D) 81x⁴ - 27x³y + 9x²y² - 3xy³ + y⁴

Question 10

Expand (5x + 3y)³ using Pascal's Triangle.

A) 125x³ + 45x²y + 75xy² + 27y³
B) 125x³ + 75x²y + 45xy² + 27y³
C) 125x³ + 225x²y + 135xy² + 27y³
D) 125x³ + 135x²y + 225xy² + 27y³

Question 11

Find the coefficient, C, of the term in the binomial expansion.
Binomial: (x + 5)⁹ Term: Cx⁶

A) 125
B) 78,750
C) 900
D) 10,500

Question 12

Find the coefficient, C, of the term in the binomial expansion.
Binomial: (x - 4y)⁶ Term: Cx³y³

A) -1,280
B) 1,280
C) 64
D) -64

Question 13

Find the coefficient, C, of the term in the binomial expansion.
Coefficient: (5x + 2y)⁸ Term: Cx⁵y³

A) 25,000
B) 3,133
C) 4,000
D) 1,400,000

Question 14

Find the coefficient, C, of the term in the binomial expansion.
Binomial: (4x - 3y)⁴ Term: Cxy³

A) 432
B) -432
C) 108
D) -108

Question 15

Evaluate the binomial coefficient.

Question 16

Expand (2x + 5)⁴ using the binomial theorem.

Question 17

In a state lottery in which 5 numbers are drawn from a possible 53 numbers, the number of possible 5 number combinations is equal to:
How many possible combinations are there?

Question 18

Expand the expression using the binomial theorem.

A)

B)

C)

D)

Question 19

Expand the expression using the binomial theorem.

A)

B)

C)

D)

Question 20

Evaluate the binomial coefficient

Question 21

Evaluate the binomial coefficient

.

Question 22

Evaluate the binomial coefficient

.

Question 23

Evaluate the binomial coefficient

.

Question 24

Evaluate the binomial coefficient

.

Question 25

Expand (x - 2)⁵ using the binomial theorem.

Question 26

Expand (3x + 5)³ using the binomial theorem.

Question 27

Expand using the binomial theorem.

Question 28

Expand (3x - y)⁴ using Pascal's Triangle.

Question 29

Expand (5x + 4y)³ using Pascal's Triangle.

Question 30

Find the coefficient, C, of the term in the binomial expansion.
Binomial: (x + 3)⁹ Term: Cx⁶

Question 31

Find the coefficient, C, of the term in the binomial expansion.
Binomial: (x - 3y)⁶ Term: Cx³y³

Question 32

Find the coefficient, C, of the term in the binomial expansion.
Coefficient: (3x + 2y)⁸ Term: Cx⁵y³

Question 33

Find the coefficient, C, of the term in the binomial expansion.
Binomial: (5x - 3y)⁴ Term: Cxy³

Question 34

Prove the statement using mathematical induction for all positive integers, n.

Question 35

Prove the statement using mathematical induction for all positive integers, n.

Question 36

Prove the statement using mathematical induction for all positive integers, n.

Question 37

Prove the statement using mathematical induction for all positive integers, n.

Question 38

Prove the statement using mathematical induction for all positive integers, n.

Question 39

Prove the statement using mathematical induction for all positive integers, n.

Question 40

Prove the statement using mathematical induction for all positive integers, n. For n > 1.
is divisible by 3

Question 41

Prove the statement using mathematical induction for all positive integers, n.

Question 42

Prove the statement using mathematical induction for all positive integers, n.

Question 43

Prove the statement using mathematical induction for all positive integers, n.

Question 44

Which relationship below can be shown to be true through mathematical induction?

A)
B)
C)
D)

Question 45

Apply mathematical induction to prove the formula.

Question 46

Prove the statement using mathematical induction for all positive integers, n.

Question 47

Determine whether the sequence is geometric. If it is, find the common ratio.
4, 8, 16, 32, 64,...

A) r = -2
B) r = 4
C) r = 2
D) r = -4

Question 48

Determine whether the sequence is geometric. If it is, find the common ratio.
-4, 8, -16, 32, -64,...

A) r = -12
B) r = -2
C) r = 12
D) r = 2

Question 49

Determine whether the sequence is geometric. If it is, find the common ratio.

A)
B)
C)
D)

Question 50

Write the first four terms of the geometric sequence with a₁ = -6 and r = -3.

A) a₁ = -6, a₂ = 9, a₃ = -12, a₄ = 15
B) a₁ = -6, a₂ = -9, a₃ = -12, a₄ = -15
C) a₁ = 6, a₂ = -18, a₃ = 54, a₄ = -162
D) a₁ = -6, a₂ = 18, a₃ = -54, a₄ = 162

Question 51

Write the first four terms of the geometric sequence with a₁ = 64 and r =

A) a₁ = -64, a₂ = -128, a₃ = -256, a₄ = -512
B) a₁ = 64, a₂ = 128, a₃ = 256, a₄ = 512
C) a₁ = -64, a₂ = -32, a₃ = -16, a₄ = -8
D) a₁ = 64, a₂ = 32, a₃ = 16, a₄ = 8

Question 52

Write the formula for the n^th term of the geometric sequence with a₁ = 6 and r = -6.

A) a_n = -6(6)^n-1
B) a_n = -6(6)ⁿ⁺¹
C) a_n = 6(-6)^n-1
D) a_n = 6(-6)ⁿ⁺¹

Question 53

Write the formula for the n^th term of the geometric sequence with a₁ = 4 and r =

A)
B)
C) a_n = 4(9)^n-1
D)

Question 54

Find the 9^th term of the geometric sequence 5, 20, 80, 320,...

A) 327,680
B) 1,310,720
C) 1,953,125
D) 1,562,500

Question 55

Find the 6th term of the geometric sequence

A)
B)
C)
D)

Question 56

Find the sum of the finite geometric series 1 + 4 + 16 + 64 + ... + 4096.

A) 4,181
B) 5,461
C) 729
D) 3,277

Question 57

Find the sum of the finite geometric series

A) 364
B) 36.5
C) -6.4
D) 72.8

Question 58

Find the sum of the infinite geometric series

A)
B)
C)
D)

Question 59

Find the sum of the infinite geometric series

A)
B)
C)
D)

Question 60

At the time she was hired, Nema's salary was $35,000 per year. If she is given an annual salary increase of 4% per year, what will her salary be after 12 years?

A) $56,036.13
B) $400,400.00
C) $53,880.89
D) $436,800.00

Question 61

Adrienne bought a condominium in 2005 for $155,000. She expects it to appreciate 4% per year. Calculate the expected value of the condominium after 14 years.

A) $258,086.39
B) $268,409.85
C) $86,800.00
D) $80,600.00

Question 62

Write the formula for the nth term of the geometric sequence with a₁ = 8 and r = -3.

Question 63

The population of a city increased at the rate of 3% every year over an eight-year period. If the population was 1,000 in 2001, what was the population in 2006?

Question 64

A bungee jumper rebounds 68% of the height jumped. Assuming the bungee jump is made with a cord that stretches to 340 feet, how far will the bungee jumper travel upward on the fourth rebound?

A) On the fourth rebound, the jumper will reach a height approximately 49 feet.
B) On the fourth rebound, the jumper will reach a height approximately 107 feet.
C) On the fourth rebound, the jumper will reach a height approximately 73 feet.
D) On the fourth rebound, the jumper will reach a height approximately 925 feet.

Question 65

Find the sum of the finite geometric series 4 + 8 + 16 + 32 + ... + 256.

Question 66

Find the sum of the finite geometric series

. Round the answer to 3 decimal places if necessary.

Question 67

Find the sum of the infinite geometric series

. Round the answer to 3 decimal places if necessary.

Question 68

Find the sum of the finite geometric series

.

Question 69

Find the sum of the finite geometric series

. Round the answer to 3 decimal places if necessary.

Question 70

Find the sum of the infinite geometric series

. Round the answer to 3 decimal places if necessary.

Question 71

Determine whether the sequence is arithmetic. If it is, find the common difference d.
6, 7, 8, 9, 10,...

A) d = -1
B) d = 1
C) d = 4
D) d = 7

Question 72

Determine whether the sequence is arithmetic. If it is, find the common difference d.
59, 55, 51, 47, 43,...

A) d = -16
B) d = 16
C) d = 4
D) d = -4

Question 73

Find the first four terms of the sequence a_n = -5n + 5. Determine whether the sequence is arithmetic, and if so, find the common difference d.

A) a₁ = 10, a₂ = 15, a₃ = 20, a₄ = 25; not arithmetic
B) a₁ = 0, a₂ = -5, a₃ = -10, a₄ = -15; not arithmetic
C) a₁ = 10, a₂ = 15, a₃ = 20, a₄ = 25; d = 5
D) a₁ = 0, a₂ = -5, a₃ = -10, a₄ = -15; d = -5

Question 74

Find the first four terms of the sequence a_n = 7(n - 3). Determine whether the sequence is arithmetic, and if so, find the common difference d.

A) a₁ = -14, a₂ = -7, a₃ = 0, a₄ = 7; not arithmetic
B) a₁ = -14, a₂ = -7, a₃ = 0, a₄ = 7; d = 7
C) a₁ = 14, a₂ = 7, a₃ = 0, a₄ = -7; not arithmetic
D) a₁ = -14, a₂ = -7, a₃ = 0, a₄ = 7; d = -7

Question 75

Find the first four terms of the sequence a_n = (-1)ⁿ⁺²(7n). Determine whether the sequence is arithmetic, and if so, find the common difference d.

A) a₁ = -7, a₂ = 14, a₃ = -21, a₄ = 28; not arithmetic
B) a₁ = -7, a₂ = 14, a₃ = -21, a₄ = 28; d = 7
C) a₁ = -7, a₂ = 14, a₃ = -21, a₄ = 28; d = -7
D) a₁ = 7, a₂ = -14, a₃ = 21, a₄ = -28; not arithmetic

Question 76

Find the general, or n^th, term of the arithmetic sequence given the first term a₁ = -7 and the common difference d = -2.

A) a_n = -5n - 2
B) a_n = 5n - 2
C) a_n = -2n - 5
D) a_n = -7n + -2

Question 77

Find the general, or n^th, term of the arithmetic sequence given the first term a₁ = 2 and the common difference d = k.

A) a_n = kn + (2 + k)
B) a_n = kn + (2 - k)
C) a_n = 2n + (2 - k)
D) a_n = kn - (2 - k)

Question 78

Find the general, or n^th, term of the arithmetic sequence given the first term a₁ = -10 and the common difference d =

A)
B)
C)
D)

Question 79

Find the 10^th term of the arithmetic sequence 9, 13, 17, 21, 25,...

A) 85
B) 53
C) 49
D) 45

Question 80

Find the 195^th term of the arithmetic sequence -5, 1, 7, 13,...

A) 1,159
B) 1,165
C) 1,171
D) -1,000