prove that it is divisible by 3 for any integer

the steps i use are

1) plug in a number to see if its true 1+2 = 3 is divisible by 3= true

2). K=N plug it in

3) K+1 =N plug it in ---- this is where I'm confused i usually have numbers for example 1+3+4+5+.......(3n+2) = n(n+1)

I'm not sure if step 3 is right because that's what i do for my usual example with numbers