Answer:
c
Step-by-step explanation:
we are given that
[tex] \displaystyle a_{n} = - 3 \: \cdot a_{n - 1} \\ a_{1} = 45[/tex]
we are already given our first term i.e 45
for second term
[tex] \displaystyle a_{2} = - 3 \: \cdot a_{2- 1} [/tex]
simplify substraction:
[tex] \displaystyle a_{2} = - 3 \: \cdot a_{1} [/tex]
since we have [tex]a_1=45[/tex]
substitute:
[tex] \displaystyle a_{2} = - 3 \: \cdot 45[/tex]
simplify multiplication:
[tex] \displaystyle a_{2} = - 135[/tex]
for third term
[tex] \displaystyle a_{3} = - 3 \: \cdot a_{3- 1} [/tex]
simplify Substraction:
[tex] \displaystyle a_{3} = - 3 \: \cdot a_{2} [/tex]
as [tex]a_2=-135[/tex]
substitute:
[tex] \displaystyle a_{3} = - 3 \: \cdot - 135[/tex]
simplify multiplication:
[tex] \displaystyle a_{3} = 405[/tex]
for forth term
[tex] \displaystyle a_{2} = - 3 \: \cdot a_{4- 1} [/tex]
simplify Substraction:
[tex] \displaystyle a_{2} = - 3 \: \cdot a_{3} [/tex]
substitute:
[tex] \displaystyle a_{2} = - 3 \: \cdot 405[/tex]
simplify multiplication:
[tex] \displaystyle a_{2} = - 1215[/tex]
hence,
the first four terms are 45,-135,405,-1215
