Question

Write the explicit formula for the geometric sequence

Answer 1

The formula
`3(4^(n-1))` represents the geometric sequence.

Explanation:

Step 1:

The value of
`a_(n)` is dependent on the value of n.

So n is independent while
`a_(n)` is dependent on n i.e. the value of
`a_(n)`depends on the value of n.

Step 2:

We substitute the values of n in the functions to check which function satisfies the values of
`a_(n)`.

If
`n = 4, a_(n) = -4(3)^(n-1) = -4 (3^(3)) = -108.` This does not equal the value of
`a_(n)`.

If
`n = 4, a_(n) = 4(3)^(n-1) =-4 (3^(3)) = 108.` This does not equal the value of
`a_(n)`.

If
`n = 4, a_(n) =3(-4)^(n-1) = 3 (-4^(3)) = -192.` This does not equal the value of
`a_(n)`.

If
`n = 4, a_(n) =3(4)^(n-1) = 3 (4^(3)) = 192.` This equals the value of
`a_(n)`.

So the fourth formula represents the geometric sequence.