Q. 45 - Calculus

Question

In Exercises 43–46 give the first five terms for a geometric sequence ${\left\{c{r}^k\right\}}_{k=0}^{\infty }$ with the specified values of $c and r.$

$c=-2, r=-3$.

Step-by-Step Solution

Answer

The first five terms are $-2,6,-18,-54,-162.$

Step 1. Given information.

The given values are $c=-2, r=-3$.

Step 2. First term.

The general sequence is $a_k=c{r}^k$

Substituting the given values,

$a_k=(-2)(-3{)}^k$

For first term, $k=0,$

Therefore,

$$\begin{gathered} a_0=(-2)(-3{)}^0 \\ =-2 \end{gathered}$$

Step 3. Remaining terms.

Now, when,

$$\begin{gathered} k=1, \\ {a}_1=(-2)(-3{)}^1=6 \\ k=2, \\ {a}_2=(-2\left)\right(-3{)}^2=-18 \\ k=3 \\ {a}_3=(-2)(-3{)}^3=-54 \\ k=4 \\ {a}_4=(-2\left)\right(-3{)}^4=162 \end{gathered}$$