Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.

n an
1 3
2 −6
3 12

an = −2(3)n − 1 where n ≥ 3

an = −3(3)n − 1 where n ≥ 3

an = 3(−2)n − 1 where n ≥ 1

an = 3(−3)n − 1 where n ≥ 1

Question

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.


n	an
1	3
2	−6
3	12

 an = −2(3)n − 1 where n ≥ 3

 an = −3(3)n − 1 where n ≥ 3

 an = 3(−2)n − 1 where n ≥ 1

 an = 3(−3)n − 1 where n ≥ 1

solomonzelman · Answer

So in other  words you are given that 
$\Large\color{blue}{     a_1 =3 }$   ,   $\Large\color{blue}{     a_2 =-6 }$    and    $\Large\color{blue}{     a_3 =12 }$

solomonzelman · Answer

So just looking at,   $\Large\color{blue}{     3,~-6,~~~12 }$   you will see that the common ratio (labelled as ` r ` ) is  `- 2 `.

solomonzelman · Answer

And it is obvious that `n ≥ 1 `

anonymous · Answer

lol yeah I thought it would be c or d

anonymous · Answer

Thank you!

solomonzelman · Answer

So now what did you choose? (making sure :)   )