Mathematical Arguments similar to Induction

Question

I need to determine whether the following arguments are true or false.

Argument 1

Argument 2

They both look somewhat similar to the axiom of induction and the axiom of strong induction. I feel like argument 1 is valid, and argument 2 is invalid, but I have no evidence or proof. Please help.

Answer 1

Argument $2$ is invalid as you cannot get $P(2)$ from the premises.

Answer 2

The first form is "induction". With the second form, the result would be that "P(n) is true for all odd n".