Question 1

Find the sum of the arithmetic sequence  that satisfies the stated conditions.

Accepted Answer

C

Question 2

Use the binomial theorem to expand and simplify.

Accepted Answer

B

Question 3

Evaluate the expression. 6!0!

Accepted Answer

The expression 6!0! is equal to 6! because 0! is defined as 1. Therefore, 6! = 720.

Question 4

Bode's sequence, defined by  can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 4th term of the sequence.

Accepted Answer

The answer of Bode's sequence, defined by  can be...

Question 5

A rubber ball is dropped from a height of 50 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

Accepted Answer

The answer of A rubber ball is dropped from a...

Question 6

Find the third term of the geometric sequence whose first two terms are 4 and 16.

Accepted Answer

The common ratio of the sequence is 16/4 = 4. Therefore, the third term is 16 * 4 = 64.

Question 7

Use the binomial theorem to expand and simplify.

Accepted Answer

The answer of Use the binomial theorem to expand and...

Question 8

Use the binomial theorem to expand and simplify.

Accepted Answer

The answer of Use the binomial theorem to expand and...

Question 9

Find the number.

Accepted Answer

The answer of Find the number. 
...

Question 10

Without expanding completely, find the term in the expansion of the expression that contains  .

Accepted Answer

The answer of Without expanding completely, find the term in...

Question 11

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Accepted Answer

The answer of Use the principle of mathematical induction to...

Question 12

Find the third term of the sequence:  is the number of decimal places in  .

Accepted Answer

The answer of Find the third term of the sequence:...

Question 13

Evaluate the expression.

Accepted Answer

The answer of Evaluate the expression. 
...

Question 14

Find the sum.

Accepted Answer

The answer of Find the sum. 
...

Question 15

Find the third term of the recursively defined infinite sequence.

Accepted Answer

The answer of Find the third term of the recursively...

Question 16

Use the principle of mathematical induction to find the factor of the expression.  Hint:

Accepted Answer

The answer of Use the principle of mathematical induction to...

Question 17

If seven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Accepted Answer

There are 7 teams, so there are 7 choices for first place. Once first place is chosen, there are 6 choices for second place. Once second place is chosen, there are 5 choices for third place. So, the total number of different ways that first, second, and third place can be decided is 7 * 6 * 5 = 210.

Question 18

Find the fourth partial sum for the given sequence.

Accepted Answer

The answer of Find the fourth partial sum for the...

Question 19

A company is to distribute $29,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

Accepted Answer

The total bonus amount is $29,000, and the difference between each salesperson's bonus is constant. Starting from the fifth salesperson with $4,600, we can calculate backwards using the arithmetic sequence formula. The sum of an arithmetic series is given by $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the total sum, $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $S_5 = 29000$, $n = 5$, and $a_5 = 4600$. To find the common difference $d$ and the first term $a_1$, we use the given information and solve for these values, leading to the sequence $7,000, $6,400, $5,800, $5,200, $4,600, which matches option D.

Question 20

Express the sum in terms of n.  (Hint: Use the theorem on sums to write the sum as  . Next, use the following formulas  and the theorem on the sum of a constant.)

Accepted Answer

The answer of Express the sum in terms of n....

Quiz 10: Sequences, Series and Probability

Find the sum of the arithmetic sequence that satisfies the stated conditions.

Use the binomial theorem to expand and simplify.

Evaluate the expression. 6!0!

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 4th term of the sequence.

A rubber ball is dropped from a height of 50 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

Find the third term of the geometric sequence whose first two terms are 4 and 16.

Use the binomial theorem to expand and simplify.

Use the binomial theorem to expand and simplify.

Find the number.

Without expanding completely, find the term in the expansion of the expression that contains .

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Find the third term of the sequence: is the number of decimal places in .

Evaluate the expression.

Find the sum.

Find the third term of the recursively defined infinite sequence.

Use the principle of mathematical induction to find the factor of the expression. Hint:

If seven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Find the fourth partial sum for the given sequence.

A company is to distribute $29,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)