Think of the generalized form of $$n$$th term

Algebra Level 4

We have 2 arithmetic progressions such that for all positive integers $$n$$, the ratio of the sum of first $$n$$ terms is $$7n+1 : 4n + 27$$.

If the ratio of the 11th terms of the AP can be expressed as $$p:q$$, where $$p$$ and $$q$$ are coprime positive integers, then find $$p+q$$.

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