-3, 12, -48, ... write the explicit and recursive formula for the geometric sequence. Use your explicit formula to calculate the 6th term in the sequence.

see below

Step-by-step explanation:

-3,12,-48,.........

the first term is =-3

The ratio is / = 12/-3 = -4

The recursive formula is

= r*

= -3 *

The explicit formula

= * r^ (n-1)

= -3 * -4^ (n-1)

To find the 6th term let n=6

= -3 * -4^ (6-1)

= -3 * -4^ (5)

= -3 * -1024 =3072

explicit formula: Un=-3*-4ⁿ⁻¹

Recursive Formula: U₆=-3*-4⁶⁻¹ = 3072

Step-by-step explanation:

Explicit formula:

Un=U₁*rⁿ⁻¹

U₁=First term

r=common ratio

Un=nth number of the sequence.

        r=12/-3=-48/12=-4

        Un=-3*-4ⁿ⁻¹

Recursive Formula for U₆

       U₆=-3*-4⁶⁻¹

       U₆=-3*-4⁵

       U₆=-3*-1024

       U₆=3072