5 - Solving: Answer: Formula P.G [tex]\boxed{A(n) = a*r^{n-1}}[/tex]
6- Solving Collecting the data of this P.G., comes:
The 1st term [tex]a_{1} = 9[/tex] The 2nd term [tex]a_{2} = 12[/tex] The 3rd term [tex]a_{3} = 16[/tex] The 4th term [tex]a_{4} = 21\frac{1}{3} = \frac{64}{3} [/tex]
It is a geometric progression (P.G), since the ratio of [tex] \frac{ a_{2} }{ a_{1} } = \frac{ a_{4} }{ a_{3}} [/tex] The ratio [tex]r = \frac {a2}{a1}[/tex] The ratio [tex]r = \frac {a4}{a3}[/tex]
The value of ratio, we have: [tex]r = \frac {a2}{a1}[/tex] [tex]r = \frac {12}{9}[/tex] simplify by 3 [tex]r = \frac {12}{9}\frac{\div3}{\div3} \to\: \boxed{\boxed{r = \frac{4}{3}}}\end{array}}\qquad\quad\checkmark[/tex] The value of ratio, we have:
