The correct option is B.
Geometric Progression,
A geometric progression is a sequence in which every next term of the sequence is found out by multiplying the previous term by a fixed ratio.
Any nth term of the sequence is found out the formula,
[tex]a_n = a_1 \times r^{n-1}[/tex],
where,
[tex]a_n[/tex] is the nth term,
[tex]a_1[/tex] is the first term,
r is the fixed common ratio.
Given to us,
Sequence, 27, 9, 3, 1.
the first term, [tex]a_1[/tex]= 27,
As we can see from the series 27, 9, 3, 1. the series is a geometric series,
And can be written as [tex]3^3,\ 3^2,\ 3^1\ ,3^0[/tex].
therefore, will follow the formula of a geometric series.
[tex]a_n = a_1 \times r^{n-1}[/tex],
Ratio
we know the value of r can be found out using the formula,
[tex]r = \dfrac{a_{n}}{a_{n-1}}}[/tex]
taking n =2,
[tex]r = \dfrac{a_{2}}{a_{2-1}}} = \dfrac{a_{2}}{a_{1}}}= \dfrac{9}{27} = \dfrac{1}{3}[/tex]
Substituting
Substituting the values in the formula of geometric progression we get,
[tex]a_n = a_1 \times r^{n-1}\\a_n = 27\times {\dfrac{1}{3}}^{n-1}\\a_n = (27)\times ({\dfrac{1}{3}})^{n-1}[/tex]
Therefore, the correct option is B.
Learn more about Substituting Geometric Progression:
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