The pattern is formed a geometric sequence
The nth term of the sequence is [tex]a_{n}=3^{n}[/tex]
Step-by-step explanation:
The formula of the nth term of a geometric sequence is:
[tex]a_{n}=ar^{n-1}[/tex] , where
- a is the first term
- r is the common ratio between the consecutive terms
∵ The pattern is 3 , 9 , 27 , 81 , 243
∵ 9 ÷ 3 = 3
∵ 27 ÷ 9 = 3
∵ 81 ÷ 27 = 3
∵ 243 ÷ 81 = 3
- There is a common ratio 3 between each two consecutive terms
∴ The pattern is formed a geometric sequence
∵ The first term is 3
∴ a = 3
∵ The common ratio is 3
∴ r = 3
- To find the nth term substitute a and r in the formula above
∵ [tex]a_{n}=ar^{n-1}[/tex]
∴ [tex]a_{n}=3(3)^{n-1}[/tex]
- Remember we add the powers of the same base with multiplication
∵ 3 × [tex]3^{n-1}[/tex] = [tex]3^{1+n-1}[/tex]
∴ 3 × [tex]3^{n-1}[/tex] = [tex]3^{n}[/tex]
∴ [tex]a_{n}=3^{n}[/tex]
∴ The nth term of the sequence is [tex]a_{n}=3^{n}[/tex]
Learn more:
You can learn more about the sequences in brainly.com/question/1522572
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