Question

what are the explicit equation and domain for geometric sequence with a first term of 4 and a second term of -8

Answer 1

`a_n=4( { (- 2)}^(n - 1) )`

for n≥1

Step-by-step explanation

The explicit equation for a geometric sequence is found using the formula:

`a_n=a_1( {r}^(n - 1) )`

where

`a_1 = 4`

is the first term and

`r =(- 8)/(4)=-2`

is the common ratio.

We substitute the values into the formula to obtain,

`a_n=4( { (- 2)}^(n - 1) )`

This is the explicit formula for the geometric sequence.

The domain is n≥1