The recursive formula for this sequence is [tex]a_{1}[/tex] = -7; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 10
Step-by-step explanation:
The recursive formula of the arithmetic sequence is:
[tex]a_{1}[/tex] = first term; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
- [tex]a_{1}[/tex] is the first term in the sequence
- [tex]a_{n}[/tex] is the nth term in the sequence
- [tex]a_{n-1}[/tex] the term before the nth term
- n is the term number
- d is the common difference
∵ The sequence is -7 , 3 , 13 , 23 , 33 , 43 , ........
∵ 3 - (-7) = 3 + 7 = 10
∵ 13 - 3 = 10
∵ 23 - 13 = 10
- There is a constant difference 10 between the consecutive terms
∴ The sequence is an arithmetic sequence
∵ The first term is -7
∴ [tex]a_{1}[/tex] = 7
∵ The common difference is 10
∴ d = 10
- Substitute in the formula above [tex]a_{1}[/tex] by -7 and d by 10
∴ [tex]a_{1}[/tex] = -7; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 10
To check the formula find the second term
∵ n = 2
∴ [tex]a_{1}[/tex] = -7; [tex]n_{2}[/tex] = [tex]n_{2-1}[/tex] + 10
∴ [tex]n_{2}[/tex] = [tex]n_{1}[/tex] + 10
∵ [tex]n_{1}[/tex] = -7
∴ [tex]n_{2}[/tex] = -7 + 10 = 3 which is right
The recursive formula for this sequence is [tex]a_{1}[/tex] = -7; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 10
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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