The first question :
[tex]a(n) = a(1) \times {q}^{n - 1} [/tex]
In which :
[tex]q = \frac{a(n)}{a(n - 1)} \\ [/tex]
Thus ;
[tex]a(12) = a(1) \times {q}^{12 - 1} [/tex]
[tex]a(1) = 6 \: \: \: and \: \: \: q = \frac{18}{6} = 3 \\ [/tex]
So :
[tex]a(12) = 6 \times {3}^{11} [/tex]
[tex]a(12) = 6 \times 177147[/tex]
[tex]a(12) = 1062882[/tex]
which mean the third option is the correct one.
_____________________________________________
Second question :
As we told in the previous question we have:
[tex]a(8) = a(1) \times {q}^{7} [/tex]
[tex]a(1) = 100 \: \: \: and \: \: \: q = \frac{20}{100} = \frac{1}{5} \\ [/tex]
So :
[tex]a(8) = 100 \times ({ \frac{1}{5} })^{7} \\ [/tex]
[tex]a(8) = 100 \times \frac{1}{78125} \\ [/tex]
[tex]a(8) = \frac{100}{78125} \\ [/tex]
[tex]a(8) = 0.00128[/tex]
So the third option is the correct one again .
There u go...
Have a great day ❤
