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kakasveta [241]
3 years ago
8

Represent the geometric series using the explicit formula.

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
7 0

The correct answer is:

b.) f(n) = 3 • (-2)^(n-1)

Further explanation:

Given sequence is:

3, -6, 12, -24, ...

We have to find the common ratio first.

Common ratio is the ratio between two consecutive terms of a geometric sequence.

It is denoted by r.

So,

Here,\\a_1=3\\a_2=-6\\a_3=12\\a_4=-24\\r=\frac{a_2}{a_1}=\frac{-6}{3}=-2\\\frac{a_3}{a_2}=\frac{12}{-6}=-2

General formula for geometric sequence is:

a_n=a_1r^{n-1}\\Here\\a_n\ is\ the\ nth\ term\\a_1\ is\ the\ first\ term\\and\\r\ is\ common\ ratio

Putting the values of a1 and r

a_n=3.(-2)^{n-1}\\f(n)=3.(-2)^{n-1}

Hence,

The correct answer is:

b.) f(n) = 3 • (-2)^(n-1)

Keywords: Geometric Sequence, Explicit formula

Learn more about geometric sequence at:

  • brainly.com/question/2048256
  • brainly.com/question/2115122

#LearnwithBrainly

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