induction proof question - not getting right answer

Question

Prove: 4 + 10 + 16 + ... + (6n -2) = n(3n + 1)

So this is my working out but my final answer shows that they don't equal ...but it should right? I can't see where I've gone wrong.

Answer 1

You're supposed to add $6(k+1)-2=6k+4$, viz. $3k^2+k+6k+4=3k^2+7k+4$. Similarly, it needs to turn out to be $(k+1)(3(k+1)+1)=(k+1)(3k+4)$, which indeed it does.