#### Arithmetic Sequences Assignment

Which table represents an arithmetic sequence?

C

The arithmetic sequence from the previous problem is 8.7, 7.3, 5.9, 4.5, 3.1, . . . . What is the common difference, d, of this sequence?d =

-1.4

What rule can be used to find the next term of the arithmetic sequence?39, 60, 81, 102, 123, . . .

C

The next term of the arithmetic sequence 39, 60, 81, 102, 123, . . . is ⇒ 144.

144

The explicit rule for an arithmetic sequence is an = -4 + (n - 1)7.What is the common difference of the arithmetic sequence?d = ⇒ 7What is the first term of the arithmetic sequence?What values of x, y, and z complete the table for the arithmetic sequence?es003-1.jpgx = ⇒ 3y = ⇒ 10z = ⇒ 17

7-431017

The first term of an arithmetic sequence is 42. The rule an = an-1 + 8 can be used to find the next term of the sequence.Explain how to write the explicit rule for the arithmetic sequence from the given information.Here, a(n) = a(n-1) + 8As the common difference = 8We know, a(n) = a + (n - 1)dSubstitute the known values, a(n) = 42 + (n - 1)8a(n) = 42 + 8n - 8a(n) = 8n + 34In short, Your explicit rule would be: 8n + 34Which did you include in your response?The rule shows that each term is 8 more than the previous term, so the common difference is 8The explicit formula of an arithmetic sequence is the initial term plus (n - 1)d.The explicit rule for this function can be found by substituting 42 for a1 and 8 for d.The explicit rule for the sequence is 42 + (n - 1)8.

Here, a(n) = a(n-1) + 8As the common difference = 8We know, a(n) = a + (n - 1)dSubstitute the known values, a(n) = 42 + (n - 1)8a(n) = 42 + 8n - 8a(n) = 8n + 34In short, Your explicit rule would be: 8n + 34

The graph shows Ms. Franklin's salary for the first few years she worked at a company.What is the explicit formula of the arithmetic sequence shown in the graph?an = If the pattern continues, what will Ms. Franklin's salary be in year 10? ⇒ 35,200

C35200

The table shows an arithmetic sequence.tableHow could you find the missing value in the table? Check all that apply.Evaluate the explicit rule for n = 4.Add 36 to the third term of the sequence.Subtract 16 from the fifth term of the sequence.What is the explicit rule for the sequence?an = -16 + (n - 1)36an = 16 + (n - 1)36an = 36 + (n - 1)(-16)an = 36 + (n - 1)16What is the fourth term of the arithmetic sequence?

A dance studio charges $17 for the first ballet class a dancer takes and$11 for each class after that.What are the first four terms of an arithmetic sequence in which an is the total amount a dancer pays, in dollars, for taking n ballet classes?What is the explicit rule for the arithmetic sequence?an = ⇒ 17 + (n - 1) ⇒ 11Keena paid a total of \$94 to take ballet classes. How many classes did she take? ⇒ 8 classes.