Answer: In Exercises 1724, use the formula for the general

Fill in each blank so that the resulting statement is true. A sequence in which each term after the first differs from the preceding term by a constant amount is called a/an ______________ sequence. The difference between consecutive terms is called the ______________ of the sequence.

Fill in each blank so that the resulting statement is true. The nth term of the sequence described in Concept Check 1 is given by the formula an ______________, where a1 is the ______________ and d is the ______________ of the sequence.

Fill in each blank so that the resulting statement is true. The sum, Sn, of the first n terms of the sequence described in Concept Check 1 is given by the formula Sn ______________, where a1 is the ______________ and an is the ______________.

Fill in each blank so that the resulting statement is true. The first term of 20 i 1 (6i 4) is ______________ and the last term is ______________.

Fill in each blank so that the resulting statement is true. The first three terms of 17 i 1 (5i 3) are ______________, ______________, and ______________. The common difference is ______________.

In Exercises 16, find the common difference for each arithmetic sequence. 2, 6, 10, 14,c

In Exercises 16, find the common difference for each arithmetic sequence. 3, 8, 13, 18,c

In Exercises 16, find the common difference for each arithmetic sequence. 7, 2, 3, 8,c

In Exercises 16, find the common difference for each arithmetic sequence. 10, 4, 2, 8,c

In Exercises 16, find the common difference for each arithmetic sequence. 714, 711, 708, 705,c

In Exercises 16, find the common difference for each arithmetic sequence. 611, 606, 601, 596,c

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 200, d 20

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 300, d 50

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 7, d 4

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 8, d 5

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 300, d 90

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 200, d 60

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 5 2 , d 1 2

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 3 4 , d 1 4

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 0.4, d 1.6

In Exercises 716, write the first six terms of each arithmetic sequence with the given first term, a1 , and common difference, d. a1 0.3, d 1.7

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a6 when a1 13, d 4.

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a16 when a1 9, d 2.

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a50 when a1 7, d 5.

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a60 when a1 8, d 6.

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a200 when a1 40, d 5.

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a150 when a1 60, d 5.

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a60 when a1 35, d 3.

In Exercises 1724, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence with the given first term, a1 , and common difference, d. Find a70 when a1 32, d 4.

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. 1, 5, 9, 13,c

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. 2, 7, 12, 17,c

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. 7, 3, 1, 5,c

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. 6, 1, 4, 9,c

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. 20, 24, 28, 32,c

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. 70, 75, 80, 85,c

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. a1 1 3 , d 1 3

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. a1 1 4 , d 1 4

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. a1 4, d 0.3

In Exercises 2534, write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for an to find a20 , the 20th term of the sequence. a1 5, d 0.2

Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22, .c

Find the sum of the first 25 terms of the arithmetic sequence: 7, 19, 31, 43, .c

Find the sum of the first 50 terms of the arithmetic sequence: 10, 6, 2, 2, .c

Find the sum of the first 50 terms of the arithmetic sequence: 15, 9, 3, 3, .c

Find 1 2 3 4 g 100, the sum of the first 100 natural numbers.

Find 2 4 6 8 g 200, the sum of the first 100 positive even integers.

Find the sum of the first 60 positive even integers.

Find the sum of the first 80 positive even integers.

Find the sum of the even integers between 21 and 45.

Find the sum of the odd integers between 30 and 54.

For Exercises 4550, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 17 i 1 (5i 3)

For Exercises 4550, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 20 i 1 (6i 4)

For Exercises 4550, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 30 i 1 (3i 5)

For Exercises 4550, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 40 i 1 (2i 6)

For Exercises 4550, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 100 i 1 4i

For Exercises 4550, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 50 i 1 (4i)

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. Find a14 b12 .

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. Find a16 b18 .

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. If {an} is a finite sequence whose last term is 83, how many terms does {an} contain?

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. If {bn} is a finite sequence whose last term is 93, how many terms does {bn} contain?

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. Find the difference between the sum of the first 14 terms of {bn} and the sum of the first 14 terms of {an}.

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. Find the difference between the sum of the first 15 terms of {bn} and the sum of the first 15 terms of {an}.

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. Write a linear function f(x) mx b, whose domain is the set of positive integers, that represents {an}.

Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 5158. Write a linear function g(x) mx b, whose domain is the set of positive integers, that represents {bn}.

Write a formula for the general term (the nth term) of the arithmetic sequence whose second term, a2 , is 4 and whose sixth term, a6 , is 16.

Write a formula for the general term (the nth term) of the arithmetic sequence whose third term, a3 , is 7 and whose eighth term, a8 , is 17.

In 1970, 11.0% of Americans ages 25 and older had completed four years of college or more. On average, this percentage has increased by approximately 0.5 each year. a. Write a formula for the nth term of the arithmetic sequence that models the percentage of Americans ages 25 and older who had or will have completed four years of college or more n years after 1969. b. Use the model from part (a) to project the percentage of Americans ages 25 and older who will have completed four years of college or more by 2019.

In 1970, 55.2% of Americans ages 25 and older had completed four years of high school or more. On average, this percentage has increased by approximately 0.86 each year. a. Write a formula for the nth term of the arithmetic sequence that models the percentage of Americans ages 25 and older who had or will have completed four years of high school or more n years after 1969. b. Use the model from part (a) to project the percentage of Americans ages 25 and older who will have completed four years of high school or more by 2019.

Company A pays $24,000 yearly with raises of $1600 per year. Company B pays $28,000 yearly with raises of $1000 per year. Which company will pay more in year 10? How much more?

Company A pays $23,000 yearly with raises of $1200 per year. Company B pays $26,000 yearly with raises of $800 per year. Which company will pay more in year 10? How much more?

a. Use the numbers shown in the bar graph to find the total cost of tuition and fees at public colleges for a four-year period from the school year ending in 2007 through the school year ending in 2010. b. The model an 395n 5419 describes the cost of tuition and fees at public colleges in academic year n, where n 1 corresponds to the school year ending in 2007, n 2 to the school year ending in 2008, and so on. Use this model and the formula for Sn to find the total cost of tuition and fees at public colleges for a four-year period from the school year ending in 2007 through the school year ending in 2010. How does this compare with the actual sum you obtained in part (a)?

a. Use the numbers shown in the bar graph to find the total cost of tuition and fees at private colleges for a four-year period from the school year ending in 2007 through the school year ending in 2010. b. The model an 1360n 20,938 describes the cost of tuition and fees at private colleges in academic year n, where n 1 corresponds to the school year ending in 2007, n 2 to the school year ending in 2008, and so on. Use this model and the formula for Sn, to find the total cost of tuition and fees at private colleges for a four-year period from the school year ending in 2007 through the school year ending in 2010. Does the model underestimate or overestimate the actual sum that you obtained in part (a)? By how much?

Use one of the models in Exercises 6566 and the formula for Sn to find the total cost of tuition and fees for your undergraduate education. How well does the model describe your anticipated costs?

A company offers a starting yearly salary of $33,000 with raises of $2500 per year. Find the total salary over a ten-year period.

You are considering two job offers. Company A will start you at $19,000 a year and guarantee a raise of $2600 per year. Company B will start you at a higher salary, $27,000 a year, but will only guarantee a raise of $1200 per year. Find the total salary that each company will pay over a ten-year period. Which company pays the greater total amount?

A theater has 30 seats in the first row, 32 seats in the second row, increasing by 2 seats each row for a total of 26 rows. How many seats are there in the theater?

A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?

What is an arithmetic sequence? Give an example with your explanation.

What is the common difference in an arithmetic sequence?

Explain how to find the general term of an arithmetic sequence.

Explain how to find the sum of the first n terms of an arithmetic sequence without having to add up all the terms.

Use the SEQ (sequence) capability of a graphing utility and the formula you obtained for an to verify the value you found for a20 in any five exercises from Exercises 2534.

Use the capability of a graphing utility to calculate the sum of a sequence to verify any five of your answers to Exercises 4550.

Rather than performing the addition, I used the formula Sn n2(a1 an) to find the sum of the first thirty terms of the sequence 2, 4, 8, 16, 32,c.

I was able to find the sum of the first fifty terms of an arithmetic sequence even though I did not identify every term.

The sequence for the number of seats per row in our movie theater as the rows move toward the back is arithmetic with d 1 so people dont block the view of those in the row behind them.

Beginning at 6:45 a.m., a bus stops on my block every 23 minutes, so I used the formula for the nth term of an arithmetic sequence to describe the stopping time for the nth bus of the day.

The sum of an arithmetic sequence cannot be negative.

The common difference for the arithmetic sequence 1, 1, 3, 5,cis 2.

An arithmetic sequence is a linear function whose domain is the set of natural numbers.

The sequence log2 2, log2 4, log2 8, log2 16, log2 32,c is arithmetic.

Give examples of two different arithmetic sequences whose fourth term, a4 , is 10.

In the sequence 21,700, 23,172, 24,644, 26,116,c, which term is 314,628?

Adegree-day is a unit used to measure the fuel requirements of buildings. By definition, each degree that the average daily temperature is below 65F is 1 degree-day. For example, an average daily temperature of 42F constitutes 23 degree-days. If the average temperature on January 1 was 42F and fell 2F for each subsequent day up to and including January 10, how many degree-days are included from January 1 to January 10?

Show that the sum of the first n positive odd integers, 1 3 5 g (2n 1), isn2.

Solve: log(x2 25) log(x 5) 3. (Section 12.4, Example 5)

Solve: x2 3x 10. (Section 11.5, Example 1)

Solve for P: A Pt P t . (Section 7.6, Example 8)

Exercises 9395 will help you prepare for the material covered in the next section. Consider the sequence 1, 2, 4, 8, 16,c. Find a2 a1 , a3 a2 , a4 a3 , and a5 a4 . What do you observe?

Exercises 9395 will help you prepare for the material covered in the next section. Consider the sequence whose nth term is an 3 5n. Find a2 a1 , a3 a2 , a4 a3 , and a5 a4 . What do you observe?

Exercises 9395 will help you prepare for the material covered in the next section. Use the formula an a13n 1 to find the 7th term of the sequence 11, 33, 99, 297,c.