Chapter 11.5, Problem 24PPS

To determine

Recursive formula for sequence

Answer to Problem 24PPS

The recursive formula is $a_n-a_{n+1}=\frac{6}{2^{n-1}}$

Explanation of Solution

Given information:

A sequence $16,10,7,5.5,4.75,\mathrm{...}$

Concept used:

A recursive formula is used to express any term of the sequence in terms of the previous term, provided that the first term is given.

Calculation:

In order to find the recursive formula for sequence $16,10,7,5.5,4.75,\mathrm{...}$ as shown below

  $\begin{array}{l}{a}_1=16\\ a_1-a_2=16-10=6=\frac{6}{1}=\frac{6}{2^0}\\ a_2-a_3=10-7=3=\frac{6}{2^1}\\ a_3-a_4=7-5.5=1.5=\frac{6}{2^2}\end{array}$

So the recursive formula is below:

  $a_n-a_{n+1}=\frac{6}{2^{n-1}}$

Thus, the recursive formula is $a_n-a_{n+1}=\frac{6}{2^{n-1}}$