Given:
The arithmetic sequence is
84, 94, 104, 114, 124,....
To find:
The recursive rule and the explicit rule for the arithmetic sequence.
Solution:
We have, the arithmetic sequence
84, 94, 104, 114, 124,....
Here,
First term : a=84
Common difference : d=94-84=10
The recursive rule for an arithmetic sequence is
[tex]f(n)=f(n-1)+d[/tex]
So, the recursive rule for the given arithmetic sequence is
[tex]f(n)=f(n-1)+10[/tex]
where, f(1)=84 and n ≥ 2.
Explicit rule for the arithmetic sequence is
[tex]f(n)=a+(n-1)d[/tex]
So, the explicit rule for the given arithmetic sequence is
[tex]f(n)=84+(n-1)10[/tex]
where, n ≥ 1.
Therefore, the recursive and explicit rules are [tex]f(n)=f(n-1)+10[/tex] and [tex]f(n)=84+(n-1)10[/tex] respectively.
