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Vikentia [17]
3 years ago
10

What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?

Mathematics
2 answers:
Misha Larkins [42]3 years ago
8 0
U can find the common ratio by dividing the 2nd term by the first term
r = -9/3 = -3

an = a1 * r^(n - 1)
a1 = 1st term = 3
r = common difference = -3
now sub
an = 3 * -3^(n - 1) <== ur formula
domain : all integers where n > = 1 <==
ella [17]3 years ago
6 0

Answer: \ a_{n}=3(-3)^{n-1}


Step-by-step explanation:

Given: A geometric sequence with its first term a_1=a=3

and second term a_2=-9

We know that the common ratio in of a geometric sequence=\frac{a_{n}}{a_{n-1}}

Thus, common ratio r=\frac{-9}{3}=-3

We know that the explicit rule for geometric sequence is written as

a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }]

Thus, the explicit rule for the given geometric sequence is \ a_{n}=3(-3)^{n-1} for every n ,a natural number.

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<h2>Explanation:</h2>

Hello! Recall that you need to write complete questions in order to get good and precise answers. However, I'll try to explain this problem in a general way. The definition of polynomial functions states:

A \ \mathbf{polynomial \ function} \ of \ x \ with \ degree \ n \ is \ given \ by:\\ \\ f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots +a_{2}x^{2}+a_{1}x+a_{0} \\ \\ where \ n \ is \ a \ nonnegative \ integer \ and \ a_{n}, a_{n-1}, \ldots a_{2}, a_{1}, a_{0} \\ with \ a_{n}\neq 0

Suppose we have the following polynomial function:

f(x)=x^3+x^2-8x-12

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(x-3) \ is \ a \ factor \ of \ f(x)=x^3+x^2-8x-12

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<h2>Learn more:</h2>

Complex zeros: brainly.com/question/13728954

#LearWithBrainly

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