Chapter 6, Problem 26CR

To determine

Whether the sequence is arithmetic geometric, or neither. If the sequence is geometric, write the next three terms and graph the sequence.

Answer to Problem 26CR

The given sequence is geometric with common ratio, $r=4$ and next three terms are $768,3072,12288$ .

Explanation of Solution

Given information: The given sequence is $3,12,48,192,\mathrm{...}$ .

Calculation:

  $\begin{array}{l}\frac{a_2}{a_1}=\frac{12}{3}=4\\ \frac{a_3}{a_2}=\frac{48}{12}=4\\ \frac{a_4}{a_3}=\frac{192}{48}=4\end{array}$

As, $\frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}=4$

Hence, it is a geometric sequence and common ratio is $4$ .

The next three terms are

  $\begin{array}{l}{a}_5=4\times 192=768\\ a_5=4\times 768=3072\\ a_5=4\times 3072=12288\end{array}$

The required graph is