Chapter 12, Problem 6CT

To determine

To find: The common ratio and the sum of the first $n$ terms.

Answer to Problem 6CT

The given sequence is neither arithmetic nor geometric

Explanation of Solution

Given information:

The given sequence is $6,12,36,\mathrm{144.............}$ .

Calculation:

Calculate the first $n$ terms,

First find the difference between the first and the second terms.

  $12-6=6$

Calculate the difference between the second and the third terms.

  $36-12=24$

Since the difference of the successive terms is not constant, we scan say that the given sequence is not arithmetic.

Calculate the ratio of the first and the second terms.

  $\begin{array}{c}r=\frac{12}{6}\\ =2\end{array}$

Calculate the ratio of the second and the third terms.

  $\begin{array}{c}r=\frac{36}{12}\\ =3\end{array}$

Since the ratio of the successive terms is not constant, we can say that the given sequence is not geometric.

Therefore, the given sequence is neither arithmetic nor geometric.