Chapter 4.7, Problem 1P

Describe the pattern in each sequence. Then find the next two terms of the sequence.

$3,6,12,24,\dots$

To determine

Describe the sequence and find the next two terms.

Answer to Problem 1P

• 3, 6, 12, 24, 48, 96

Explanation of Solution

Given Data:

3, 6, 12, 24........

Calculation:

  $\begin{array}{l}\text{The series is in Geometric Sequence}\\ \text{Thus, the sequence is given by:}\\ a_n=a{r}^{(n-1)}\\ \text{Now,}\\ 3,6,12,\mathrm{24........}\\ \text{Gives}\\ a_n=a{r}^{(n-1)}=3\times 2^{(n-1)}\\ \text{In a geometric sequence, the terms are seperated by a common ratio }r.\\ \text{Here }r=2\Rightarrow r=\left(\frac{a_2}{a_1}\right)\\ \text{Thus,}\\ a_4=r\times a_3(4^{th}\text{ Term)}\\ a_3=r\times a_2{\text{ (3}}^{rd}\text{ Term)}\\ \text{and so on}\mathrm{.....}\\ \text{Therefore,}\\ a_5=2\times a_4=2\times 24=48\\ a_6=2\times a_5=2\times 48=96\end{array}$

Conclusion:

Thus the required series is:

3,6,12,24,48,96........