Chapter 8.3, Problem 9E

To determine

To check: Whether the sequence is geometric.

Answer to Problem 9E

No, the given sequence is not geometric.

Explanation of Solution

Given information:

The sequence:

  $0.2,3.2,-12.8,51.2,-204.8,\mathrm{.....}$

Formula used:

The geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Check for GP:

  $\frac{a_2}{a_1}=\frac{a_3}{a_2}$

Where $a_1,a_2,a_3$ are first, second and third term of GP respectively.

  $0.2,3.2,-12.8,51.2,-204.8,\mathrm{.....}$

Recall that Check for GP is:

  $\begin{array}{l}\frac{a_2}{a_1}=\frac{a_3}{a_2}\\ \\ a_1=0.2\\ a_2=3.2\\ a_3=-12.8\end{array}$

  $\begin{array}{l}\frac{3.2}{0.2}=\frac{-12.8}{3.2}\\ \\ 16=-4\\ \\ LHS\ne RHS\end{array}$

the ratio of second term to first term is not equal to the ratio of third term to second term.

No, the given sequence is not geometric.