Option B - the explicit formula is [tex]4(2^{n} - 1)[/tex] is correct.
We have the following sequence - 4, 8, 16, 32, 64, ...,
We have to find the explicit formula.
What is the formula to find the nth term of an Geometric progression ?
The formula to find the nth term of an Geometric Progression with first term - a and common ratio - r is :
[tex]S_{n} =\frac{a(r^{n}-1)}{r-1}[/tex]
The sequence given in the question is -
4, 8, 16, 32, 64, ...., nth term
First we will check whether the sequence given is Geometric progression or not. For this, the ratio of : [tex]\frac{8}{4} =\frac{16}{8}[/tex] should be equal. We can see that the ratio is same and is equal to 2.
Now, a = 4 and r = 2, substituting the values in the formula -
[tex]S_{n}[/tex] = [tex]\frac{4(2^{n} - 1) }{2 -1} = 4(2^{n}-1)[/tex]
Hence, the explicit formula is [tex]4(2^{n} - 1)[/tex]
To solve more questions on Geometric Progression, visit the link below-
https://brainly.com/question/14320920
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