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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