sequences and series - Arithmetic Progression.

Q. The ratio between the sum of $n$ terms of two A.P's is $3n+8:7n+15$. Find the ratio between their $12$th term.

My method:

Given:

As this applies for any term:

But this is not the answer. The actual answer is $\frac7{16}$. I know how to obtain that answer.

But why is my solution wrong? Its probably the concept I guess.