Arithmetic Sequences Assignment

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

144

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

C 35200

Which table represents an arithmetic sequence?

C

The table shows an arithmetic sequence. table How 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)36 an = 16 + (n - 1)36 an = 36 + (n - 1)(-16) an = 36 + (n - 1)16 What is the fourth term of the arithmetic sequence?

A D D 84

The sixth term of an arithmetic sequence is 3 2 , and the twelfth term is 5 2 . What is the common difference of the arithmetic sequence? The common difference is ⇒ 1/6. What is the explicit rule for the arithmetic sequence?

1/6 C

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) ⇒ 11 Keena paid a total of $94 to take ballet classes. How many classes did she take? ⇒ 8 classes.

C 17 11 8

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) + 8 As the common difference = 8 We know, a(n) = a + (n - 1)d Substitute the known values, a(n) = 42 + (n - 1)8 a(n) = 42 + 8n - 8 a(n) = 8n + 34 In short, Your explicit rule would be: 8n + 34 Which did you include in your response? The rule shows that each term is 8 more than the previous term, so the common difference is 8 The 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) + 8 As the common difference = 8 We know, a(n) = a + (n - 1)d Substitute the known values, a(n) = 42 + (n - 1)8 a(n) = 42 + 8n - 8 a(n) = 8n + 34 In short, Your explicit rule would be: 8n + 34

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

7 -4 3 10 17