Here’s why i ask. In your first ratio, ak+1 is an odd number (since k is even), so this means that a+k is also odd and that n is odd too (rewrite ak+1 = n(a+k) to see why that must be true). So n and a are odd numbers.
By a similar argument, bk+1 is odd, so b+k+2 is odd, and hence b is odd.
Now if a and b are odd, and a+b+c=12, then c must be even. The last ratio can be rewritten ck+2=n(c+k+3)=even=(odd)(odd). That’s a problem. So it looks to me that there can be no integer solutions here.
Maybe I made a mistake somewhere, or maybe you had a typo when you entered the problem. But that looks right to me.