The explicit rule for the [tex]nth[/tex] term of the given sequence is [tex]a_n=9(4)^{n-1}[/tex].
Given:
The given sequence is [tex]9,36,144,576[/tex].
To find:
The explicit rule for the [tex]nth[/tex] term of the given sequence.
Explanation:
the first term of the sequence is [tex]9[/tex].
The ratios of two consecutive terms are:
[tex]\dfrac{36}{9}=4[/tex]
[tex]\dfrac{144}{36}=4[/tex]
[tex]\dfrac{576}{144}=4[/tex]
The given sequence is a geometric sequence because the sequence has a common ratio [tex]4[/tex].
The explicit formula for the [tex]nth[/tex] term is:
[tex]a_n=ar^{n-1}[/tex]
Where, [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio.
Substituting [tex]a=9,r=4[/tex], we get
[tex]a_n=9(4)^{n-1}[/tex]
Therefore, the explicit rule for the [tex]nth[/tex] term of the given sequence is [tex]a_n=9(4)^{n-1}[/tex].
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