Question

match each sequence with one of the recursive definitions. note that only the part of the definition showing the relatopmship between the current term and the precious term is giving so as not to give away the solutions. one of the sequences matches two recursive definitions. a. a(n) = a(n-1)-4 b. b(n)=b(n-1)+0 c. c(n)= -1/2 x c(n-1) d. d(n)=1xd(n-1)

Answer 1

9514 1404 393

Answer:

1. A
2. C
3. B, D

Explanation:

1. The common difference is -4, which matches recursive relation A.

2. Signs alternate, so the common ratio must be negative, matching recursive relation C.

3. The common difference is 0, and the common ratio is 1, so both relations B and D are a match.

_____

An arithmetic sequence with common difference d can be described by the recursive relation ...

f(n) = f(n-1) +d

A geometric sequence with common ratio r can be described by the recursive relation ...

f(n) = r·f(n-1)

One typically has to look at only the first three terms to determine if they have a constant difference or a constant ratio.