What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12? an = 4(−3)n − 1; all integers where n ≥ 1 an = 4(−3)n − 1; all integers where n ≥ 0 an = 4(36)n − 1; all integers where n ≥ 1 an = 4(36)n − 1; all integers where n ≥ 0

The geometric sequence is given by:
an=ar^(n-1)
where:
a=first term
r=common ratio
n is the nth term
given that a=4, and second term is -12, then
r=-12/4=-3
hence the formula for this case will be:
an=4(-3)^(n-1)
where n≥1

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SerenaBochenek SerenaBochenek · Answer 2 · 2018-12-31T09:17:31+01:00

Answer:

[tex]a_{n} = 4 \times (-3)^{n-1}[/tex]; all integers where n ≥ 1

Step-by-step explanation:

We are given that the first term of the sequence is 4 i.e. [tex]a_{1} =4[/tex] and second term is -12 i.e. [tex]a_{2} = -12[/tex].

Now, the nth term of geometric sequence is given by,

[tex]a_{n} = a_{n-1} \times r[/tex], where r is the common ratio of the sequence.

So, using the given values we get,

[tex]a_{2} = a_{1} \times r[/tex]

i.e. [tex]r = \frac{a_{2} }{a_{1} }[/tex]

i.e. [tex]r = \frac{-12}{4}[/tex]

i.e. r = -3.

Now the explicit formula for the geometric equation is given by,

[tex]a_{n} = a_{1} \times r^{n-1}[/tex].

i.e. [tex]a_{n} = 4 \times(-3)^{n-1}[/tex], where [tex]n\geq 1[/tex]

Hence option first is correct.