Question

For the following geometric sequence, find the explicit formula. {1, -3, 9, ...} an = -3 · an - 1 where a1 = 1 an = -3 · an - 1 where a1 = -1 an = -1 · (-3)n - 1 an = (-3)n - 1

Answer 1

{ 1,-3,9...}

an = a1 * r^(n-1)
a1 = first term = 1
r = common ratio = -3

so ur formula is : an = 1 * -3^(n-1)

Answer 2

The correct option is 4.

Explanation:

The given geometric sequence is

{1, -3, 9, ...}

Here the first term of the sequence is 1 and the common ratio is

`r=(a_2)/(a_1)=(-3)/(1)=-3`

The explicit formula of a geometric sequence is

`a_n=ar^(n-1)`

In the given geometric sequence a=1 and r=-3.

Substitute a=1 and r=-3 in the above formula.

`a_n=(1)(-3)^(n-1)`

`a_n=(-3)^(n-1)`

The explicit formula of given geometric sequence is
`a_n=(-3)^(n-1)`.

Therefore the correct option is 4.