Answer:
9 × (½)^(n-2)
Step-by-step explanation:
It's a Geometric sequence with:
First term: 18
Common ratio: 9/18 = ½
Nth term: 18 × (½)^(n-1)
9×2 × (½)^(n-1)
9 × (½^-1) × (½)^(n-1)
9 × (½)^(n-2)
A recursive formula for given sequence is [tex]\bold{a_n=\frac{a_{n-1}}{2}}[/tex], [tex]n\geq 2[/tex] and [tex]a_1=18[/tex]
"A sequence is an ordered list of elements that follow a specific pattern or function."
The recursive formula for a geometric sequence with common ratio r and first term [tex]a_1[/tex] is:
[tex]a_n=r\times a_{n-1}[/tex] for [tex]n\geq 2[/tex]
Given sequence: 18, 9, 4.5
The first term of the sequence [tex]a_1=18[/tex]
[tex]\frac{9}{18}=\frac{1}{2}[/tex]
and [tex]\frac{9}{4.5}=\frac{1}{2}[/tex]
This means the ratio between consecutive terms is same.
So, given sequence is the geometric sequence with common ratio [tex]r=\frac{1}{2}[/tex]
After substituting values in the formula for a geometric sequence,
[tex]\bold{a_n=\frac{1}{2} \times a_{n-1}}[/tex] , [tex]n\geq 2[/tex]
Therefore, a recursive formula for the given sequence is,
[tex]\bold{a_n=\frac{a_{n-1}}{2}}[/tex] , [tex]n\geq 2[/tex] and [tex]a_1=18[/tex]
Learn more about geometric sequence here:
https://brainly.com/question/11266123
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