Respuesta :

Answer:

The 10th term is 39366

Step-by-step explanation:

The n-th term in a geometric progression is

[tex]T_n = a {r}^{n - 1} [/tex]

The third term is

[tex]T_3 = a {r}^{2} = 18[/tex]

The 6th term is

[tex]T_6 = a {r}^{5} = 486[/tex]

Let us take the ratio:

[tex] \frac{T_6}{T_3} = \frac{a {r}^{5} }{a {r}^{2} } = \frac{486}{18} = 27[/tex]

This means that:

[tex] {r}^{3} = 27[/tex]

[tex]r = \sqrt[3]{27} = 3[/tex]

Put this into the 3rd term

[tex]a \times {3}^{2} = 18[/tex]

[tex]9a = 18[/tex]

[tex]a = 2[/tex]

The 10th term is:

[tex]T_ {10} = a {r}^9[/tex]

[tex]T_ {10} = 2 \times {3}^{9}= 39366[/tex]