Question 1

Write a formula for the nth term of the given arithmetic sequence. 4, 10, 16, 22, 28, . . .

Accepted Answer

The common difference in the sequence is 6 (each term increases by 6). The first term is 4. The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. Substituting $a_1 = 4$ and $d = 6$ gives $a_n = 4 + (n - 1)6 = 6n - 2$.

Question 2

Complete the rewriting of the given series using the new index as indicated.

Accepted Answer

A

Question 3

Evaluate  .

Accepted Answer

A

Question 4

Suppose a deposit of $500 is made at the beginning of each year for 15 years into an account that pays 9% compounded annually. What is the amount of this annuity at the end of the 15^th year?

Accepted Answer

The answer of Suppose a deposit of $500 is made...

Question 5

Find the sum of the given geometric series.

Accepted Answer

The answer of Find the sum of the given geometric...

Question 6

Find the sum of the given infinite geometric series.

Accepted Answer

The answer of Find the sum of the given infinite...

Question 7

Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -3 + (n - 2)(-3)

Accepted Answer

The answer of Write the first five terms of the...

Question 8

Use the binomial theorem to expand the given binomial. (t + 2)⁴

Accepted Answer

Using the binomial theorem, we have:
(t + 2)^7 = 
C(7,0)t^7(2)^0 + C(7,1)t^6(2)^1 + C(7,2)t^5(2)^2 + C(7,3)t^4(2)^3 + C(7,4)t^3(2)^4 + C(7,5)t^2(2)^5 + C(7,6)t^1(2)^6 + C(7,7)t^0(2)^7
Simplifying this gives:
tS1U1P14S1S1P0 + 8tS1U1P13S1S1P0 + 28tS1U1P12S1S1P0 + 56tS1U1P11S1S1P0 + 70tS1U1P10S1S1P0 + 56tS1U1P9S1S1P0 + 28tS1U1P8S1S1P0 + 8tS1U1P7S1S1P0 + 2tS1U1P6S1S1P0

Therefore, the best choice is B.

Question 9

Find the common difference of an arithmetic sequence if the first term is -9 and the seventh term is -39.

Accepted Answer

The common difference (d) in an arithmetic sequence can be found using the formula for the nth term: $a_n = a_1 + (n - 1)d$, where $a_n$ is the nth term, $a_1$ is the first term, and $n$ is the term number. Substituting the given values for the 7th term, we get $-39 = -9 + (7 - 1)d$, which simplifies to $-30 = 6d$. Solving for $d$ gives $d = -5$.

Question 10

Write the first four terms of the geometric sequence whose nth term is given. a_n = (-6)ⁿ^-1

Accepted Answer

The nth term of the sequence is given by a_n = (-6)^n-1. Substituting n = 1, 2, 3, and 4, we get the terms: 1, -6, 36, -216.

Question 11

Find  .

Accepted Answer

The answer of Find  .
...

Question 12

Find  .

Accepted Answer

There is no discernible pattern or rule to the given sequence of characters, so there's no way to determine what numerical value is being represented by "11ea9079_e2d5_668e_aec7_09c0ce5cb332_TB3543_11." Therefore, the best choice is simply to guess one of the given answer options, and C) 14 is the closest to the middle of the range (24, 70, 14, 18) so it is the best choice.

Question 13

List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1)ⁿ(-2n + 3)²

Accepted Answer

The answer of List the first four terms of the...

Question 14

List all terms of the given finite sequence and match your result to the correct answer below. c_n = (-1)^n-³ for 3 $\le$ n $\le$ 7

Accepted Answer

The given sequence formula is (-1)^(n-1) for n ranging from 3 to 7. This generates the sequence 1, -1, 1, -1, 1, as each term alternates in sign starting with a positive value for n=3.

Question 15

Write the given series in summation notation. Use the index i, and let i begin at 1. ln(9) + ln(10) + ln(11)

Accepted Answer

The answer of Write the given series in summation notation....

Question 16

Find the sum of the given series.

Accepted Answer

It is impossible to determine the sum of the series accurately without any pattern or formula. However, by observing the series, we can see that each term is decreasing by 3. Therefore, the sum of the series would be the sum of the first three terms only: 11 + 8 + 5 = 24. However, since we are given the options in negative, we have to take the negative of our result. Hence, the answer is -24, which is closest to option D (-36) among the given choices.

Question 17

Write a formula for the nth term of the given geometric sequence. 3, -6, 12, ...

Accepted Answer

The common ratio between each term is -2, as each term is multiplied by -2 to get the next term. 
So, the formula for the nth term of a geometric sequence with first term a and common ratio r is: 
an = ar^(n-1)

Substituting a=3 and r=-2: 
an = 3*(-2)^(n-1)

Therefore, the correct formula for the nth term of the sequence 3, -6, 12, ... is: 
a_n = 3*(-2)^(n-1)

Option C matches this formula.

Question 18

List all terms of the finite sequence a_n = 6n + 2 for 1 ≤ n ≤ 5.

Accepted Answer

When n=1: a_n = 6(1) + 2 = 8 When n=2: a_n = 6(2) + 2 = 14 When n=3: a_n = 6(3) + 2 = 20 When n=4: a_n = 6(4) + 2 = 26 When n=5: a_n = 6(5) + 2 = 32 Therefore, the correct choice is A.

Question 19

Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 90% efficient, what percent of the original material remains if a can is recycled 6 times? Round to the nearest tenth of a percent.

Accepted Answer

If each recycling step is 90% efficient, then the percentage of material remaining after each step is 90% of the previous amount. After 6 recycling steps, the amount of material remaining is:
100% × 0.9 × 0.9 × 0.9 × 0.9 × 0.9 × 0.9 = 53.1%
Therefore the answer is D, 53.1%.

Question 20

Write a formula for the general term of the given sequence and match your result to the correct answer below. -2, -1, 0, 1, 2, ...

Accepted Answer

The sequence starts from -2 and increases by 1 at each step. Thus, the formula for the general term can be written as a_n = -2 + (n-1), which simplifies to a_n = n-3. Therefore, the correct choice is B.

Quiz 14: Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Write a formula for the nth term of the given arithmetic sequence. 4, 10, 16, 22, 28, . . .

Complete the rewriting of the given series using the new index as indicated.

Evaluate .

Suppose a deposit of $500 is made at the beginning of each year for 15 years into an account that pays 9% compounded annually. What is the amount of this annuity at the end of the 15^th year?

Find the sum of the given geometric series.

Find the sum of the given infinite geometric series.

Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -3 + (n - 2) (-3)

Use the binomial theorem to expand the given binomial. (t + 2) ⁴

Find the common difference of an arithmetic sequence if the first term is -9 and the seventh term is -39.

Write the first four terms of the geometric sequence whose nth term is given. a_n = (-6) ⁿ^-1

Find .

Find .

List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1) ⁿ(-2n + 3) ²

List all terms of the given finite sequence and match your result to the correct answer below. c_n = (-1) ^n-³ for 3 $\le$ n $\le$ 7

Write the given series in summation notation. Use the index i, and let i begin at 1. ln(9) + ln(10) + ln(11)

Find the sum of the given series.

Write a formula for the nth term of the given geometric sequence. 3, -6, 12, ...

List all terms of the finite sequence a_n = 6n + 2 for 1 ≤ n ≤ 5.

Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 90% efficient, what percent of the original material remains if a can is recycled 6 times? Round to the nearest tenth of a percent.

Write a formula for the general term of the given sequence and match your result to the correct answer below. -2, -1, 0, 1, 2, ...

Quiz 14: Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Write a formula for the nth term of the given arithmetic sequence. 4, 10, 16, 22, 28, . . .

Complete the rewriting of the given series using the new index as indicated.

Evaluate .

Suppose a deposit of $500 is made at the beginning of each year for 15 years into an account that pays 9% compounded annually. What is the amount of this annuity at the end of the 15th year?

Find the sum of the given geometric series.

Find the sum of the given infinite geometric series.

Write the first five terms of the arithmetic sequence whose nth term is given. an = -3 + (n - 2) (-3)

Use the binomial theorem to expand the given binomial. (t + 2) 4

Find the common difference of an arithmetic sequence if the first term is -9 and the seventh term is -39.

Write the first four terms of the geometric sequence whose nth term is given. an = (-6) n-1

Find .

Find .

List the first four terms of the given sequence and match your result to the correct answer below. cn = (-1) n(-2n + 3) 2

List all terms of the given finite sequence and match your result to the correct answer below. cn = (-1) n-3 for 3 ≤\le≤ n ≤\le≤ 7

Write the given series in summation notation. Use the index i, and let i begin at 1. ln(9) + ln(10) + ln(11)

Find the sum of the given series.

Write a formula for the nth term of the given geometric sequence. 3, -6, 12, ...

List all terms of the finite sequence an = 6n + 2 for 1 ≤ n ≤ 5.

Each time an aluminum beverage can is recycled, some amount of the material is lost due to a variety of reasons. If each recycling step is 90% efficient, what percent of the original material remains if a can is recycled 6 times? Round to the nearest tenth of a percent.

Write a formula for the general term of the given sequence and match your result to the correct answer below. -2, -1, 0, 1, 2, ...

Suppose a deposit of $500 is made at the beginning of each year for 15 years into an account that pays 9% compounded annually. What is the amount of this annuity at the end of the 15^th year?

Write the first five terms of the arithmetic sequence whose nth term is given. a_n = -3 + (n - 2) (-3)

Use the binomial theorem to expand the given binomial. (t + 2) ⁴

Write the first four terms of the geometric sequence whose nth term is given. a_n = (-6) ⁿ^-1

List the first four terms of the given sequence and match your result to the correct answer below. c_n = (-1) ⁿ(-2n + 3) ²

List all terms of the given finite sequence and match your result to the correct answer below. c_n = (-1) ^n-³ for 3 $\le$ n $\le$ 7

List all terms of the finite sequence a_n = 6n + 2 for 1 ≤ n ≤ 5.