(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(b) The explicit rule for the sequence is: [tex]a_{n}=15n-10[/tex]
Step-by-step explanation:
The form of the recursive rule of an arithmetic sequence sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex] , where
The form of the explicit rule of nth term of an arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
∵ The sequence is 5, 20, 35, 50, ….......
∵ 20 - 5 = 15 , 35 - 20 = 15 and 50 - 35 = 15
∴ The sequence is an arithmetic sequence with a common
difference 15
∵ The form of the recursive rule of the arithmetic sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex]
∵ First term = 5
∵ d = 15
∴ [tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
∵ The form of the explicit rule of nth term of an arithmetic
sequence is [tex]a_{n}=a+(n-1)d[/tex]
∵ a = 5 and d = 15
- Substitute these values in the rule
∴ [tex]a_{n}=5+(n-1)15[/tex]
- Simplify the right hand side
∴ [tex]a_{n}=5+15n-15[/tex]
- Add like terms
∴ [tex]a_{n}=15n-10[/tex]
(b) The explicit rule for the sequence is [tex]a_{n}=15n-10[/tex]
Learn more;
You can learn more about the sequences in brainly.com/question/3280369
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