Respuesta :
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Answer:
b(n) = 12 * 2^(n-1) where n >=1
Discussion:
12* 2 = 24 (second term in sequence)
24 * 2 = 48 (third term in sequence)
48 *2 = 96 (fourth term in the sequence)
So b(n) = 12 * 2^(n-1) where n >=1
b(1) = 12 * 2^ 0 = 12 * 1 = 12
b(2) = 12 * 2^(2-1) =12 * 2 - 24,
Thank you,
MrB
An explicit formula for the geometric sequence 12, 24, 48, 96 using the common ratio 2 is,
[tex]b_n=12 \times (2)^{n-1}[/tex]
What is geometric sequence?
Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
It can be given as,
[tex]a_n=a_1\times r^{n-1}[/tex]
Here, [tex]a[/tex] is the first term of the sequence and [tex]r[/tex] is the common ratio.
Given information-
The geometric sequence given in the problem is,
12, 24, 48, 96,
To find the explicit formula for the geometric sequence, first find the common ratio. Let common ratio is r.
Thus,
[tex]r=\dfrac{24}{12}=2\\r=\dfrac{48}{24}=2\\r=\dfrac{96}{48}=2[/tex]
Thus the common ratio of the geometric sequence is 2. The first term of the given sequence is 12. Put the value in the formula as,
[tex]b_n=12 \times (2)^{n-1}[/tex]
Thus the an explicit formula for the geometric sequence 12,24,48,96 is,
[tex]b_n=12 \times (2)^{n-1}[/tex]
Learn more about the geometric sequence here;
https://brainly.com/question/1509142
