Chapter 7.10, Problem 39PFA

To determine

The recursive formula for the given sequence.

Answer to Problem 39PFA

The recursive formula is $a_1=-2$ , $a_n=-2a_{n-1}$

Explanation of Solution

Given information: A table given with n and $a_n$ values. When n=1, $a_n=-2$ , when n=2, $a_n=4$ , when n=3, $a_n=-8$ , when n=4, $a_n=16$ .

Calculation:

Here given, the first term $a_1=-2$ , second term $a_2=4$ , third term $a_3=-8$ , fourth term $a_4=16$ .

So, it can be written as,

  $\begin{array}{l}{a}_2=4=-2\times -2=a_1\times -2=-2a_1\\ a_3=-8=4\times -2=a_2\times -2=-2a_2\\ a_4=16=-8\times -2=a_3\times -2=-2a_3\end{array}$

  $\therefore$ The recursive formula is $a_n=-2a_{n-1}$ , $a_1=-2$ .

Option A is correct.