Answer:
The recursive rule is [tex]f(1)[/tex] = first term; [tex]f_({n})[/tex] = [tex]f_({n-1})[/tex] + d
f(1) = 55; [tex]f_{20}[/tex] = [tex]f_{19}[/tex] + 10
The explicit rule is f(n) = f(1) + (n - 1)d
f(20) = 245
Step-by-step explanation:
The recursive rule of the arithmetic sequence is
[tex]a_{1}[/tex] = first term; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
Where:
- [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] is the term before the nth term
- d is the common difference.
The explicit rule of the arithmetic sequence is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
where:
- [tex]a_{1}[/tex] is the first term in the sequence
- [tex]a_{n}[/tex] is the nth term in the sequence
- d is the common difference
∵ The first 4 terms of the sequence are 55, 65, 75, 85
∴ [tex]a_{1}[/tex] = 55
∵ d = 65 - 55
∴ d = 10
∵ We need to find the 20th term
∴ n = 20
∵ The recursive rule is [tex]f(1)[/tex] = first term; [tex]f_({n})[/tex] = [tex]f_({n-1})[/tex] + d
→ Substitute the values of [tex]a_{1}[/tex], n, and d in recursive rule
∴ f(1) = 55; [tex]f_{20}[/tex] = [tex]f_{19}[/tex] + 10
∵ The explicit rule is f(n) = f(1) + (n - 1)d
→ Substitute the values of n and d to find it
∴ f(20) = 55 + 19(10) = 245
∴ f(20) = 245
