Question

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.


n an
1 | 3
2 | −6
3 | 12

Answer 1

geometric sequcne

regular formula: $a_n=a_1(r)^{n-1}$
explicit formula: $a_n=\frac{a_1}{r}r^n$
an=nth term
a1=first term
r=common ratio or what we multiply each term by to get the next term
n=which term

when n=1, an=3

so the first term is 3
so a1=3
each term is times -2 of the previus
so r=-2
so the explicit formula is $a_n=\frac{3}{-2}(-2)^n$
or
$a_n=\frac{-3(-2)^n}{2}$


the domain is the numbers you can use
we have to use only natural numbers (or counting numbers)
that is 1,2,3,4,5, etc

the domain is all natural numbers
the explicit formula is $a_n=\frac{-3(-2)^n}{2}$ or $f(n)=\frac{-3(-2)^n}{2}$

Answer 2

Answer:

The domain is all real numbers