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