Answer:
The first four terms of the sequence are:
[tex]5,-20,80,-320[/tex]
Step-by-step explanation:
We're already given the first term:
[tex]a_1=5[/tex]
We'll calculate the next three terms of the sequence as following:
[tex]\begin{gathered} a_2=-4a_{2-1} \\ \rightarrow a_2=-4a_1 \\ \rightarrow a_2=(-4)(5) \\ \Rightarrow a_2=-20 \\ \\ a_3=-4a_{3-1} \\ \operatorname{\rightarrow}a_3=-4a__2 \\ \operatorname{\rightarrow}a_3=(-4)(-20) \\ \Rightarrow a_3=80 \\ \\ a_4=-4a_{4-1} \\ \rightarrow a_4=-4a_3 \\ \rightarrow a_4=(-4)(80) \\ \Rightarrow a_4=-320 \end{gathered}[/tex]
Therefore, we can conclude that the first four terms of the sequence are:
[tex]5,-20,80,-320[/tex]
