Answer:
4.5, -27, 162,-972, 5832
Step-by-step explanation:
The given recursive definition is,
[tex]a_n=-6a_{n-1}, a_1=4.5[/tex]
This will form a geometric sequence with first term 4.5 and common ratio r=-6.
When n=2, we have:
[tex]a_2=-6a_1 \\ \implies \: a_2=-6 \times 4.5 = - 27[/tex]
When n=3, we get:
[tex]a_3=-6a_2 \\ \implies \: a_3=-6 \times - 27 = 162[/tex]
When n=4, we get:
[tex]a_4=-6a_3 \\ \implies \: a_4=-6 \times 162 = - 972[/tex]
When n=5, we get:
[tex]a_5=-6a_4 \\ \implies \: a_5=-6 \times - 972 = 5832[/tex]
Therefore the first five terms are:
4.5, -27, 162,-972, 5832
