Question

1) Determine o termo geral de cada PG.
a) (1,5....)
b) (2,3,...)​

Answer 1

Termo geral:

$\boxed{a_n=a_kq^{n-k}}$

a)

$\left\{a_1,a_2,\dots\right\}=\left\{1,5,\dots\right\}$

$a_2=a_1q\ \to\ q=\dfrac{a_2}{a_1}=\dfrac{5}{1}\ \to\ \boxed{q=5}$

$a_n=a_1q^{n-1}\ \to\ a_n=1(5^{n-1})\ \to\ \boxed{a_n=5^{n-1}}$

b)

$\left\{a_1,a_2,\dots\right\}=\left\{2,3,\dots\right\}$

$a_2=a_1q\ \to\ q=\dfrac{a_2}{a_1}=\dfrac{3}{2}\ \to\ \boxed{q=\dfrac{3}{2}}$

$a_n=a_1q^{n-1}\ \to\ a_n=2\bigg(\dfrac{3}{2}\bigg)^{n-1}\ \to\ \boxed{a_n=\dfrac{3^{n-1}}{2^{n-2}}}$