This Sum Is That; That Sum Is This

Algebra Level 4

For distinct numbers \(p\) and \(q\), consider an arithmetic progression such that

  • the sum of the first \(p\) terms is equal to \(q\), and
  • the sum of the first \(q\) terms is equal to \(p\).

What is the sum of the first \(p+ q\) terms?

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