Answer:
[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex]
Step-by-step explanation:
the explicit formula for 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
here a₁ = 12 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then explicit formula is
[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex]
