Question

Write a recursive definition for the sequence 8,6,4,2...

Answer 1

Answer:

1. a1 = 8; an= an-1 - 2
2. an = -3 + 4(n-1)

Step-by-step explanation:

1. The first step in problem solving is to look at the given information. Here, you can see that each number in the sequence is 2 less than the one before it.

In the expression ...

  an = an-1 - 2

the term an-1 means the previous term, the term just before term an. So, this equation means the term of the sequence is 2 less than the one before it. Since this matches the description of the sequence, this recursive relation is part of the correct answer. (The other part is the definition of the first term of the sequence: a1 = 8.)

The recursive definition is ...

  $a_1=8;\ a_n=a_{n-1}-2$

__

2. The given sequence has first term a1 = -3, and common difference d = 4. That is, each term is 4 more than the previous one. The explicit formula for an arithmetic sequence is ...

  an = a1 +d(n -1)

Filling in the given values gives you the explicit formula ...

  $a_n=-3+4(n-1)$