Question

For the following geometric sequence find the explicit formula. {12, -6, 3, ...}​

Answer 1

`a_(n)` = 12
`(-(1)/(2)) ^(n-1)`

Explanation:

The nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 12 and r =
`(a_(2) )/(a_(1) )` =
`(-6)/(12)` = -
`(1)/(2)` , then

`a_(n)` = 12
`(-(1)/(2)) ^(n-1)` ← explicit formula

Answer 2

It's geometric sequence where a_1=12, q=-\dfrac{1}{2}a

1

=12,q=−

2

1

So a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}a

n

=12⋅(−

2

1

)

n−1