Math discussion assignment
Discuss with class and try to solve 2-3 problems each
Be sure to solve some of the Textbook application problems using two important formulas, the first one for the nth term of the sequence and the second one for the SUM of the first n terms of the sequence:
Formula #1. an = a1 + (n-1)d, where a1 = the first term and d = common difference
Formula #2. which is the formula for a1 + a2 + a3 + … + an
Please solve each of the following problems in one post for grade:
Problem # 63. 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?
Problem #64. 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?
Problem #68. 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.
Use a system of two equations in two variables, a1 and d,
to solve Exercises 59-60.
Problem #59. 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.
Problem # 60. 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.
Problem (by myself)). Write a formula for the general term (the nth term) of the arithmetic sequence whose 37th term, a37, is 256 and whose 92th term, a92, is 641.
Problem # 61. 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.
Problem # 62. 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.
#69. 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?
#70. A theater has 30 seats in the first row, 32 seats in the second row, increasing by 2 seats per row for a total of 26 rows. How many seats are there in the theater?
#71. 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?
1. What is an Arithmetic Sequence? What are the first term and the common difference? Give a good example.
2. Define the general term in arithmetic Sequence and refer its Key ingredients.
3. Write a formula for the general term (the nth term an = ?) of the arithmetic sequence whose second term, a2 = 4 and whose sixth term, a6, = 16.
4. Write a formula for the general term (the nth term) of the arithmetic sequence whose third term,
a3, = 7 and whose eighth term, a8 = 17.
(What formula do we use to solve the above two problems? Remember, you need to find the nth term in terms of n, i.e., as a function of n like for example
an = 3n-2 or an = 2n+1, but no guessing )
5. What do we mean by an arithmetic Series verses an arithmetic Sequence? Define by an example.
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