Projections for the U.S. population, ages 85 and older, are shown in the following

In Exercises 14, write the first four terms of each sequence whose general term is given.an = 7n - 4

In Exercises 14, write the first four terms of each sequence whose general term is given.an = (-1) n n + 2 n + 1

In Exercises 14, write the first four terms of each sequence whose general term is given.an = 1 (n - 1)!

In Exercises 14, write the first four terms of each sequence whose general term is given.. an = (-1) n+1 2n

In Exercises 56, find each indicated sum.a 5 i=1 (2i 2 - 3)

In Exercises 56, find each indicated sum.a 4 i=0 (-1) i+1i!

In Exercises 78, express each sum using summation notation. Use i for the index of summation.1 3 + 2 4 + 3 5 + g + 15 17

In Exercises 78, express each sum using summation notation. Use i for the index of summation.43 + 53 + 63 + g + 133

In Exercises 911, write the first six terms of each arithmetic sequence.a1 = 7, d = 4

In Exercises 911, write the first six terms of each arithmetic sequence.a1 = -4, d = -5

In Exercises 911, write the first six terms of each arithmetic sequence.. a1 = 3 2 , d = - 1 2

In Exercises 1214, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence.Find a6 when a1 = 5, d = 3.

In Exercises 1214, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence.Find a12 when a1 = -8, d = -2.

In Exercises 1214, use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of each sequence.Find a14 when a1 = 14, d = -4.

In Exercises 1518, 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 1518, 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 = 200, d = -20

In Exercises 1518, 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 = -12, d = - 1 2

In Exercises 1518, 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.15, 8, 1, -6,c

Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, .c

Find the sum of the first 15 terms of the arithmetic sequence: -6, -3, 0, 3, .c

Find 3 + 6 + 9 + g + 300, the sum of the first 100 positive multiples of 3.

In Exercises 2224, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.a 16 i=1 (3i + 2)

In Exercises 2224, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.a 25 i=1 (-2i + 6)

In Exercises 2224, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.a 30 i=1 (-5i)

The graphic indicates that there are more eyes at school. 2005 58% Percentage of United States Students Ages 1218 Seeing Security Cameras at School 2001 39% Source: U.S. Department of Education In 2001, 39% of students ages 1218 reported seeing one or more security cameras at their school. On average, this has increased by approximately 4.75% per year since then. a. Write a formula for the nth term of the arithmetic sequence that describes the percentage of students ages 1218 who reported seeing security cameras at school n years after 2000. b. Use the model to project the percentage of students ages 1218 who will report seeing security cameras at school by the year 2013.

A company offers a starting salary of $31,500 with raises of $2300 per year. Find the total salary over a ten-year period.

A theater has 25 seats in the first row and 35 rows in all. Each successive row contains one additional seat. How many seats are in the theater?

In Exercises 2831, write the first five terms of each geometric sequence.a1 = 3, r = 2

In Exercises 2831, write the first five terms of each geometric sequence.a1 = 1 2 , r = 1 2

In Exercises 2831, write the first five terms of each geometric sequence.a1 = 16, r = - 1 4

In Exercises 2831, write the first five terms of each geometric sequence.a1 = -5, r = -1

In Exercises 3234, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence.Find a7 when a1 = 2, r = 3.

In Exercises 3234, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence.Find a6 when a1 = 16, r = 1 2 .

In Exercises 3234, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence.Find a5 when a1 = -3, r = 2.

In Exercises 3537, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a8 , the eighth term of the sequence.1, 2, 4, 8,c

In Exercises 3537, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a8 , the eighth term of the sequence.100, 10, 1, 1 10 ,c

In Exercises 3537, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a8 , the eighth term of the sequence.12, -4, 4 3 , - 4 9 ,c

Find the sum of the first 15 terms of the geometric sequence: 5, -15, 45, -135, .c

Find the sum of the first 7 terms of the geometric sequence: 8, 4, 2, 1, .c

In Exercises 4042, use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum.a 6 i=1 5i

In Exercises 4042, use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum.a 7 i=1 3(-2) i

In Exercises 4042, use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum.a 5 i=1 2a 1 4 b i-1

In Exercises 4346, find the sum of each infinite geometric series.9 + 3 + 1 + 1 3 + g

In Exercises 4346, find the sum of each infinite geometric series.2 - 1 + 1 2 - 1 4 + g

In Exercises 4346, find the sum of each infinite geometric series.-6 + 4 - 8 3 + 16 9 - g

In Exercises 4346, find the sum of each infinite geometric series.. a i=1 5(0.8) i

In Exercises 4748, express each repeating decimal as a fraction in lowest terms.0.6

In Exercises 4748, express each repeating decimal as a fraction in lowest terms.0.47

Projections for the U.S. population, ages 85 and older, are shown in the following table. 2000 Projected Population in millions 4.2 5.9 8.3 11.6 16.2 22.7 Year 2010 2020 2030 2040 2050 Actual 2000 population Source: U.S. Census Bureau a. Show that the U.S. population, ages 85 and older is projected to increase geometrically. b. Write the general term of the geometric sequence describing the U.S. population ages 85 and older, in millions, n decades after 1990. c. Use the model in part (b) to project the U.S. population, ages 85 and older, in 2080.

A job pays $32,000 for the first year with an annual increase of 6% per year beginning in the second year. What is the salary in the sixth year? What is the total salary paid over this six-year period? Round answers to the nearest dollar.

In Exercises 5152, use the formula for the value of an annuity and round to the nearest dollar.You spend $10 per week on lottery tickets, averaging $520 per year. Instead of buying tickets, if you deposited the $520 at the end of each year in an annuity paying 6% compounded annually, a. How much would you have after 20 years? b. Find the interest.

In Exercises 5152, use the formula for the value of an annuity and round to the nearest dollar.To save for retirement, you decide to deposit $100 at the end of each month in an IRA that pays 5.5% compounded monthly. a. How much will you have from the IRA after 30 years? b. Find the interest.

A factory in an isolated town has an annual payroll of $4 million. It is estimated that 70% of this money is spent within the town, that people in the town receiving this money will again spend 70% of what they receive in the town, and so on. What is the total of all this spending in the town each year?

In Exercises 5455, evaluate the given binomial coefficient. 11 8

In Exercises 5455, evaluate the given binomial coefficient. 90 2

In Exercises 5659, use the Binomial Theorem to expand each binomial and express the result in simplified form.(2x + 1) 3

In Exercises 5659, use the Binomial Theorem to expand each binomial and express the result in simplified form.(x2 - 1) 4

In Exercises 5659, use the Binomial Theorem to expand each binomial and express the result in simplified form.. (x + 2y) 5

In Exercises 5659, use the Binomial Theorem to expand each binomial and express the result in simplified form.. (x - 2) 6

In Exercises 6061, write the first three terms in each binomial expansion, expressing the result in simplified form.(x2 + 3) 8

In Exercises 6061, write the first three terms in each binomial expansion, expressing the result in simplified form.(x - 3) 9

In Exercises 6263, find the indicated term in each expansion.. (x + 2) 5 ; fourth term

In Exercises 6263, find the indicated term in each expansion.(2x - 3) 6 ; fifth term