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Anna35 [415]
3 years ago
14

For the following geometric sequence find the explicit formula. {12, -6, 3, ...}

Mathematics
2 answers:
vivado [14]3 years ago
7 0
It's geometric sequence where a_1=12, q=-\dfrac{1}{2}

So a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}

enyata [817]3 years ago
4 0

Answer:

a_n=12*(-\frac{1}{2})^{n-1}

Step-by-step explanation:

We are asked to write an explicit formula for the given geometric sequence.

We know that explicit formula for a given geometric sequence is in form a_n=a_1*r^{n-1}, where,

a_n=\text{ nth term of sequence},

a_1=\text{ 1st term of sequence},

r = Common ratio.

n = Number of terms of sequence.

To find common ratio, we will divide any term of our given sequence by its previous term.

r=-\frac{-6}{12}=-\frac{1}{2}

a_n=12*(-\frac{1}{2})^{n-1}

Therefore, our required formula would be a_n=12*(-\frac{1}{2})^{n-1}.

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