Answer:
[tex]a_{n}[/tex] = 96[tex](-1.5)^{n-1}[/tex]
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio.
Both values have to be found.
Using
a₂ = - 144, then
ar = - 144 → (1)
a₅ = 486, then
a[tex]r^{4}[/tex] = 486 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{486}{-144}[/tex]
r³ = - 3.375 ( take the cube root of both sides )
r = - 1.5
Substitute r = - 1.5 into (1)
- 1.5a = - 144 ( divide both sides by - 1.5 )
a = 96
Hence explicit formula is
[tex]a_{n}[/tex] = 96[tex](-1.5)^{n-1}[/tex]
