Algebra and Trigonometry: Sequences, Probability, and Counting Theory flashcards

Question 1

What does a recursive formula for a sequence use to define each term?

Accepted Answer

The previous term or terms

Question 2

What must every recursive formula for a sequence state?

Accepted Answer

The initial term (or terms)

Question 3

What does an explicit formula for a sequence use to define each term?

Accepted Answer

The term's position in the sequence

Question 4

What are the values of 0! and 1!?

Accepted Answer

0! = 1 and 1! = 1

Question 5

What is an arithmetic sequence?

Accepted Answer

A sequence where any two consecutive terms differ by a constant

Question 6

Explicit formula for term n of an arithmetic sequence?

Accepted Answer

a_n = a_1 + d(n − 1)

Question 7

What is a geometric sequence?

Accepted Answer

A sequence where the ratio of any two consecutive terms is a constant

Question 8

Recursive formula for a geometric sequence, common ratio r?

Accepted Answer

a_n = r·a_(n−1), for n ≥ 2

Question 9

Explicit formula for term n of a geometric sequence?

Accepted Answer

a_n = a_1·r^(n−1)

Question 10

What is a series?

Accepted Answer

The sum of a sequence's terms

Question 11

Which Greek letter does summation notation use?

Accepted Answer

Sigma

Question 12

Formula for the sum of the first n terms of an arithmetic series?

Accepted Answer

S_n = n(a_1 + a_n)/2

Question 13

Sum of an infinite geometric series whose ratio satisfies −1 < r < 1?

Accepted Answer

S = a_1/(1 − r)

Question 14

What does the Addition Principle say about events with no common outcomes?

Accepted Answer

If one can occur in m ways and the other in n ways, the first or second can occur in m + n ways

Question 15

What is another name for the Multiplication Principle?

Accepted Answer

The Fundamental Counting Principle

Question 16

In a permutation, does order matter?

Accepted Answer

Yes; a permutation is a selection in which order matters

Question 17

Formula for the number of permutations of n distinct objects taken r at a time?

Accepted Answer

P(n, r) = n!/(n − r)!

Question 18

Formula for the number of combinations of n distinct objects taken r at a time?

Accepted Answer

C(n, r) = n!/(r!(n − r)!)

Question 19

How many subsets does a set of n distinct objects have?

Accepted Answer

2^n

Question 20

Number of permutations of n objects that are not all distinct?

Accepted Answer

n!/(r_1! r_2! … r_k!)

Question 21

Which combination count equals the binomial coefficient (n choose r)?

Accepted Answer

C(n, r)

Question 22

What is the (r + 1)th term of the binomial expansion of (x + y)^n?

Accepted Answer

(n choose r) x^(n − r) y^r

Question 23

What is a sample space?

Accepted Answer

The set containing every possible outcome of an experiment

Question 24

What is an event, in probability?

Accepted Answer

Any subset of a sample space

Question 25

What are mutually exclusive events?

Accepted Answer

Events with no outcomes in common

Question 26

What do the probabilities in a probability model add up to?

Accepted Answer

1

Question 27

Probability of the union of two events E and F?

Accepted Answer

P(E ∪ F) = P(E) + P(F) − P(E ∩ F)

Question 28

Probability of the complement of an event E?

Accepted Answer

P(E′) = 1 − P(E)

Algebra and Trigonometry: Sequences, Probability, and Counting Theory flashcards

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