Answer:
see explanation
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
(1)
a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then
[tex]a_{n}[/tex] = 2 [tex]-3)^{n-1}[/tex]
(2)
a₁ = 5 and r = [tex]\frac{10}{5}[/tex] = 2 , then
[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]
