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Enter the explicit rule for the geometric sequence.



1/4, 1/2, 1, 2, 4, …

Sagot :

Answer:

[tex]a_n = (\frac{1}{4})2^{n-1}[/tex]

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is the same, and this quotient is given by q.

The explicit rule of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

1/4, 1/2, 1, 2, 4

This means that [tex]a_1 = \frac{1}{4}[/tex], and:

[tex]q = \frac{4}{2} = \frac{2}{1} = \frac{1}{\frac{1}{2}} = \frac{\frac{1}{2}}{\frac{1}{4}} = 2[/tex]

So the explicit rule is:

[tex]a_n = (\frac{1}{4})2^{n-1}[/tex]

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