Difficulty in solving a question regarding the sum of two arithmetic sequences. 
Hey guys, I am having a problem solving a question regarding the sum of two linear sequeneces. Using the equation $S_n=\frac{n}{2}[2a(n-1)d] = 15=5n$, whenever I do try to solve it, I get $25-5n=\frac{30-10n}{n}$. Further simplifying this into a quadratic equation, I get $n=1\space and \space n=6$. However, this is misleading and instead, leaves me even more confused. Can someone point out what I am doing wrong, thanks.

I think you have misunderstood the question. It just wants you to add together two terms: the $n$th term of A plus the $n$th term of B. You do not need to work out the sum of either sequence.
