Chapter 11.5, Problem 26PPS

To determine

Recursive formula for sequence

Answer to Problem 26PPS

The recursive formula is $a_{n+1}={\left(a_n\right)}^2-1$

Explanation of Solution

Given information:

A sequence $4,15,224,50175,\mathrm{...}$

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 $4,15,224,50175,\mathrm{...}$ as shown below

  $\begin{array}{c}{a}_1=4\\ a_2={\left(a_1\right)}^2-1\\ ={\left(4\right)}^2-1=16-1\\ =15\\ a_3={\left(a_2\right)}^2-1\\ ={\left(15\right)}^2-1=225-1\\ =224\\ a_4={\left(a_3\right)}^2-1\\ ={\left(224\right)}^2-1=50176-1\\ =50175\end{array}$

So the recursive formula is below:

  $a_{n+1}={\left(a_n\right)}^2-1$

Thus, the recursive formula is $a_{n+1}={\left(a_n\right)}^2-1$