Answer:
explicit definition: [tex]a_n=5n-4[/tex]
recursive definition: [tex]a_n=a_{n-1}+5[/tex]
Step-by-step explanation:
Given arithmetic sequence: 1, 6, 11, 16, 21 ...
Therefore,
- first term a = 1
- common difference d = 5
Using the general form of arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
[tex]\implies a_n=1+(n-1)5[/tex]
[tex]\implies a_n=1+5n-5[/tex]
[tex]\implies a_n=5n-4[/tex]
or [tex]a_n=a_{n-1}+5[/tex]
