Recursive Formulas

Question 1

An arithmetic sequence has the explicit formula an = 7n – 17. What is the value of a1?

Revolt · Accepted Answer

-10

Question 2

Which is the recursive formula for this arithmetic sequence?

Revolt · Accepted Answer

an = an – 1 + 7 where a1 = –10

Question 3

Find the first three terms of the sequence described by the following recursive formula:an = 3an – 1 + 2 where a4 = 20a1 =

Revolt · Accepted Answer

4/3; 6

Question 4

, , , 2 1 4

Revolt · Accepted Answer

Part 1: 144; Part 2: 36; Part 3: 9

Question 5

−3 , ⇒ -12 , , ,

Revolt · Accepted Answer

Part 2: -72; Part 3: -576; Part 4: -5,760

Question 6

Suppose that an insect population’s density, in thousands per acre, during year n, can be modeled by the recursive formula:a1 = 8 an = 2.9an – 1 – 0.2(an – 1)2Which of the following describes what is happening to the insect population for the first five years?

Revolt · Accepted Answer

The population alternates between increasing and decreasing.

Question 7

If a sequence contains only whole numbers, which of these sequences could include the term 27, if a1 does not equal 27?

Revolt · Accepted Answer

an = 2an – 1 + 1; an = 3an – 1; an = an – 1 + 6

Question 8

toothpicks.

Revolt · Accepted Answer

Part 1: 4; Part 2: 10; Part 3: 16

Question 9

In an arithmetic sequence, a17 = -40 anda28 = -73. Explain how to use this information to write a recursive formula for this sequence.

Revolt · Accepted Answer

Answer

Question 10

Which did you include in your explanation?

Revolt · Accepted Answer

The difference between the given terms is –73 – (–40) = –33.; The common difference is –3.

Recursive Formulas Answers

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