Answer :
Answer:
The recursive formulas for the following sequence is [tex]a_n=a_{n-1}+5[/tex].
Step-by-step explanation:
The given explicit formula is
[tex]a_n=2+(n-1)5[/tex]
Find the (n-1)th term of the sequence.
[tex]a_{n-1}=2+(n-1-1)5[/tex]
[tex]a_{n-1}=2+(n-2)5[/tex] .... (1)
The given explicit formula can be written as
[tex]a_n=2+(n-1(-2+2))5[/tex]
[tex]a_n=2+(n-2(-1+2))5[/tex]
[tex]a_n=2+(n-2+1)5[/tex]
Use distributive property.
[tex]a_n=2+(n-2)5+5[/tex]
Using equation (1), we get
[tex]a_n=a_{n-1}+5[/tex]
Therefore the recursive formulas for the following sequence is [tex]a_n=a_{n-1}+5[/tex].