Precalculus: Sequences, Probability and Counting Theory flashcards

Question 1

What is a single number in a sequence called?

Accepted Answer

A term.

Question 2

What kind of formula gives each term of a sequence from the term or terms before it?

Accepted Answer

A recursive formula.

Question 3

What must a recursive formula for a sequence also state?

Accepted Answer

The initial term or terms of the sequence.

Question 4

What is n factorial (n!)?

Accepted Answer

The product of all positive integers from 1 to n.

Question 5

What are the values of 0! and 1!?

Accepted Answer

Both equal 1.

Question 6

What is an arithmetic sequence?

Accepted Answer

A sequence in which consecutive terms always differ by the same constant.

Question 7

What is the explicit formula for the nth term of an arithmetic sequence with first term a1 and common difference d?

Accepted Answer

a_n = a1 + d(n − 1)

Question 8

Give the recursive rule for an arithmetic sequence whose common difference is d.

Accepted Answer

a_n = a_(n−1) + d, for n ≥ 2

Question 9

What is a geometric sequence?

Accepted Answer

A sequence in which the ratio of each term to the term before it is constant.

Question 10

How can the common ratio of a geometric sequence be found?

Accepted Answer

Divide any term by the term before it.

Question 11

What is the explicit formula for the nth term of a geometric sequence with first term a1 and common ratio r?

Accepted Answer

a_n = a1 · r^(n − 1)

Question 12

What is the nth partial sum of a sequence?

Accepted Answer

The sum of its first n terms.

Question 13

Which Greek letter is used in summation notation?

Accepted Answer

Sigma (Σ).

Question 14

What is the sum of the first n terms of an arithmetic series?

Accepted Answer

S_n = n(a1 + a_n)/2

Question 15

What is the sum of the first n terms of a geometric series with ratio r ≠ 1?

Accepted Answer

S_n = a1(1 − r^n)/(1 − r)

Question 16

For which common ratios r does an infinite geometric series have a sum?

Accepted Answer

When −1 < r < 1.

Question 17

What is the sum of an infinite geometric series with first term a1 and −1 < r < 1?

Accepted Answer

a1/(1 − r)

Question 18

What does the Addition Principle of counting state?

Accepted Answer

If two events share no outcomes and can happen in m and n ways, then one or the other can happen in m + n ways.

Question 19

What is another name for the Multiplication Principle of counting?

Accepted Answer

The Fundamental Counting Principle.

Question 20

What is the difference between a permutation and a combination?

Accepted Answer

In a permutation the order of the selected objects matters; in a combination it does not.

Question 21

What is the formula for P(n, r), the permutations of n distinct objects taken r at a time?

Accepted Answer

P(n, r) = n!/(n − r)!

Question 22

What is the formula for C(n, r), the combinations of n distinct objects taken r at a time?

Accepted Answer

C(n, r) = n!/(r!(n − r)!)

Question 23

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

Accepted Answer

2^n

Question 24

Which counting quantity is the binomial coefficient (n choose r) equal to?

Accepted Answer

C(n, r), the number of combinations of n objects taken r at a time.

Question 25

In the expansion of (x + y)^n, what is the (r + 1)th term?

Accepted Answer

(n choose r) · x^(n − r) · y^r

Question 26

What is the sample space of an experiment?

Accepted Answer

The set of all possible outcomes of the experiment.

Question 27

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

Accepted Answer

1

Question 28

What is P(E ∪ F) for any two events E and F?

Accepted Answer

P(E ∪ F) = P(E) + P(F) − P(E ∩ F)

Question 29

What are mutually exclusive events?

Accepted Answer

Events that share no outcomes.

Question 30

What is P(E′), where E′ is the complement of event E?

Accepted Answer

P(E′) = 1 − P(E)

Precalculus: Sequences, Probability and Counting Theory flashcards

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