Chapter 12.1, Problem 6AYU

The sequence $a_1\text{ = 5}$, $a_n\text{ = 3}{a}_{n-\text{ 1}}$ is an example of $a\left(n\right)$ _____ sequence.

(a) alternating       (b) recursive

(c) Fibonacci       (d) summation

To determine

To fill: The sequence $a_1=5,a_n=3a_{n-1}$ is an example of a $\left(n\right)$ _____ sequence.

a. Alternating.

b. Recursive.

c. Fibonacci.

d. Summation.

Answer to Problem 6AYU

The sequence $a_1=5,a_n=3a_{n-1}$ is an example of a $\left(n\right)$ recursive sequence.

Explanation of Solution

A second way of defining a sequence is to assign a value to the first (or the first few) term(s) and specify the nth term by a formula or equation that involves one or more of the terms preceding it. Such sequences are said to be defined recursively, and the rule or formula is called a recursive formula.