Chapter 13, Problem 12GR

Solution

To find: The next two terms of the given sequence and to find the formula for nth term.

The next two terms are $-216,-343$ .

  $a_n=-n^3$ .

It is an explicit formula.

Given:

  $-1,-8,-27,-64,-125,\mathrm{......}$

Calculation:

The terms in the given sequence can be written as,

  ${\left(-1\right)}^3,{\left(-2\right)}^3,{\left(-3\right)}^3,{\left(-4\right)}^3,{\left(-5\right)}^3,\mathrm{.....}$

So, the next two terms are

  $\begin{array}{c}{\left(-6\right)}^3=-216\\ {\left(-7\right)}^3=-343\end{array}$

Now, the formula for the nth term is

  $a_n=-n^3$

It is an explicit formula.