Chapter 6.6, Problem 20E

To determine

To write: A recursive rule for the given sequence

Answer to Problem 20E

  $a_n=a_{n-1}-11,a_1=35$

Explanation of Solution

Given:

n	1	2	3	4
$a_n$	35	24	13	2

The value of $a_n$ for $n=1$ is 35. Hence we must have $a_1=35$

It can be observed that the given values of $a_n$ forms an arithmetic progression with a common difference of -11.

A recursive relation for an arithmetic progression with common difference d is given by $a_n=a_{n-1}+d$ .

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

  $a_n=a_{n-1}-11,a_1=35$ .