Answer
See below.
Work Step by Step
Proofs using mathematical induction consists of two steps:
1) The base case: here we prove that the statement holds for the first natural number.
2) The inductive step: assume the statement is true for some arbitrary natural number $n$ larger than the first natural number, then we prove that then the statement also holds for $n + 1$.
Hence here:
1) For $n=1: 2=0.5(1)(3(1)+1)$.
2) Assume for $n=k: 2+5+...+(3k-1)=0.5k(3k+1)$. Then for $n=k+1$:
$2+5+...+(3k-1)+(3k+2)=0.5k(3k+1)+(3k+2)=1.5k^2+0.5k+3k+2=0.5(k+1)(3k+4)=0.5(k+1)(3(k+1)+1).$
Thus we proved what we wanted to.