Chapter 6.6, Problem 21E

To determine

To write: A recursive rule for the given sequence

Answer to Problem 21E

  $a_n=2a_{n-1},a_1=1$

Explanation of Solution

Given:The bacterial cells grows as

n	1	2	3	4
$a_n$	1	2	4	8

where n is in hours.

The value of $a_n$ for $n=1$ is 1. Hence we must have $a_1=1$

It can be observed that the given values of $a_n$ forms a geometric progression with a common ratio of 2.

A recursive relation for ageometric progression with common difference d is given by $a_n=d{a}_{n-1}$ .

Hence, for the given problem the recursive relation must be given by:

  $a_n=2a_{n-1},a_1=1$ .