Question

Find the explicit formula for the geometric sequence cn given below. Note that c1=6.

Answer 1

The explicit formula for the geometric sequence $c_{n}$ is

$c_{n}=6(\frac{-1}{3})^{n-1}$

Step-by-step explanation:

The formula of the nth term of a geometric sequence is

$a_{n}=a(r)^{n-1}$ , where:

• a is the first term of the sequence
• r is the common ratio between the consecutive terms

The geometric sequence of $c_{n}$ is 6 , -2 , $\frac{2}{3}$ , $\frac{-2}{9}$ , $\frac{2}{27}$

∵ $c_{1}$ = 6

∵ $r=\frac{c_{2}}{c_{1}}$

∵ $c_{2}$ = -2

∴ $r=\frac{-2}{6}$

- Divide both term by 2 to simplify it

∴ $r=\frac{-1}{3}$

∵ $c_{n}=c_{1}(r)^{n-1}$

- Substitute the value of $c_{1}$ and r in the rule above

∴ $c_{n}=6(\frac{-1}{3})^{n-1}$

The explicit formula for the geometric sequence $c_{n}$ is

$c_{n}=6(\frac{-1}{3})^{n-1}$

Learn more:

You can learn more about the geometric sequence in brainly.com/question/1522572

#LearnwithBrainly