Question

In a geometric sequence, a2= -144 and a5=486. Write the explicit formula for this sequence

Answer 1

Answer: an=96(-3/2)^n-1

Explanation:

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Answer 2

`a_(n)` = 96
`(-1.5)^(n-1)`

Explanation:

The n th term of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

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
`r^(4)` = 486 → (2)

Divide (2) by (1)

`(ar^4)/(ar)` =
`(486)/(-144)`

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

`a_(n)` = 96
`(-1.5)^(n-1)`