Question

Study the geometric sequence {-4, -84, -1764, -37044, ...}.

What is the explicit formula for the sequence?
(21)(-4)(n-1)
O an = (-21)(4)(n-1)
O an = (-4) (21)(n-1)
O an = (4)(-21)(n-1)

Answer 1

`\bold{a_n=(-4)21^(n-1)}`

Explanation:

`a_1=-4\,,\ a_2=-84\,,\ a_3=-1764\,,\ a_4=-37044\quad\implies\ \ r=21`

{-84:(-4)=21 and -1764:(-84)=21 and -37044:(-1764)=21}

geometric sequence formula:
`a_n=a_1r^(n-1)`

`a_1=-4\quad and \ \ r=21`

`a_n=(-4)21^(n-1)`