I assume you mean
Add 3k+2 to both sides:
It is shown.
You can put in the usual details.
Prove by mathematical induction that 2+5+8+...+(3k-1) = 1/2n(3n+1)
k^2 = 2+5+8+...+(3k-1)
(k+1)^2 = 2+5+8+...+ 3(k+1) + [3(k+1)-1]
(k+1)^2 = 2+5+8+...+ 3(k+1) + 3k + 2
(k+1)^2 = k^2+3k+2
k^2 + 2k +1 =/ k^2 +3k +2
Did I do something wrong or is the problem not true?