Just wanted to check that this proof is set out correctly and that the last statement is logically correct:

Question

AnswerUse mathematical induction to prove that is divisible by 15 for all positive integers n.

Let be is divisible by 15.

Assuming to be true [1] ( ),

From [1],

Therefore if is divisible by 15, then so is ,

When , . Therefore the basis case holds true.

Therefore by mathematical induction,