MHB How do you solve the recurrence relation P(n) = 1 + 5n by induction?

[Fernando Revilla]

I quote a question from Yahoo! Answers

Solve P(n) = 1 + 5n by induction?
Closed form solution: P(n) = 1 + 5n
from, P(n) = {1 if n = 1
P(n-1) + 5 if n > 1}

I have given a link to the topic there so the OP can see my response.

 

[Fernando Revilla]

The recurrence relation is $p(n)=p(n-1)+5,\; p(1)=1$. Then, $p(n)=1+5n$ is a solution.

Basis Step $p(1)=1+5\cdot 0=1$.

Induction Step Suppose the relation is true for $n$. Then, $p(n)=1+5n$, so
$$p(n+1)=1+5(n+1)=1+5n+5=p(n)+5$$

As a consqeuence, the relation is true for $n+1$.