The recursive formula is [tex]a_{1}[/tex] = 14; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3
The explicit formula is [tex]a_{n}=3n+11[/tex]
Step-by-step explanation:
The recursive formula of the nth term of the arithmetic sequence is
[tex]a_{1}[/tex] = first term; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d, where
The explicit formula of the nth term of the arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
∵ The arithmetic sequence is 14, 17, 20, 23, 26
∴ The first term is 14
∵ 17 - 14 = 3
∴ The common difference is 3
∵ The recursive formula is [tex]a_{1}[/tex] = first term; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
∵ [tex]a_{1}[/tex] = 14
∵ d = 3
∴ [tex]a_{1}[/tex] = 14; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3
The recursive formula is [tex]a_{1}[/tex] = 14; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3
∵ The explicit formula is [tex]a_{n}=a+(n-1)d[/tex]
∵ a = 14
∵ d = 3
∴ [tex]a_{n}=14+(n-1)3[/tex]
- Simplify the right hand side
∴ [tex]a_{n}=14+3n-3[/tex]
- Add like terms
∴ [tex]a_{n}=3n+11[/tex]
The explicit formula is [tex]a_{n}=3n+11[/tex]
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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