Respuesta :
Answer:
Fourth term: [tex]a_4 = 9 * (\frac{\sqrt{3}}{3})^{(4 - 1)}[/tex] = [tex]9 * (\frac{\sqrt{3}}{3})^{3}[/tex] = [tex]\sqrt{3}[/tex]
Fifth term: [tex]a_5 = 9 * (\frac{\sqrt{3}}{3})^{(5 - 1)}[/tex] = [tex]9 * (\frac{\sqrt{3}}{3})^{4}[/tex] = 1
Sixth term: [tex]a_6 = 9 * (\frac{\sqrt{3}}{3})^{(6 - 1)} = 9 * (\frac{\sqrt{3}}{3})^{5} =\frac{\sqrt{3}}{3}[/tex]
Step-by-step explanation:
The geometric progression is:
[tex]9, 3 \sqrt{3}, 3...[/tex]
The first term, a, is 9
To find the common ratio, r, all we have to do is divide a term by its preceding term.
Let us divide the second term by the first:
[tex]r = \frac{3\sqrt{3}}{9}\\ \\r = \frac{\sqrt{3}}{3}[/tex]
That is the common ratio.
Geometric progression is given generally as:
[tex]a_n = ar^{(n - 1)}[/tex]
where a = first term
r = common ratio
[tex]a_n[/tex] = nth term
We need to find the 4th, 5th and 6th terms.
Fourth term: [tex]a_4 = 9 * (\frac{\sqrt{3}}{3})^{(4 - 1)}[/tex] = [tex]9 * (\frac{\sqrt{3}}{3})^{3}[/tex] = [tex]\sqrt{3}[/tex]
Fifth term: [tex]a_5 = 9 * (\frac{\sqrt{3}}{3})^{(5 - 1)}[/tex] = [tex]9 * (\frac{\sqrt{3}}{3})^{4}[/tex] = 1
Sixth term: [tex]a_6 = 9 * (\frac{\sqrt{3}}{3})^{(6 - 1)} = 9 * (\frac{\sqrt{3}}{3})^{5} =\frac{\sqrt{3}}{3}[/tex]
