# Arithmetic progressions

Algebra Level 2

Consider an arithmetic progression of $$n$$ terms such that:

• The sum of the second term and the $$n^{\text{th}}$$ term is 1005.
• The sum of the first term and $${(n - 1)}^{\text{th}}$$ term is 991.
• The sum of all terms of this set is 71357.

Calculate the value of $$n$$.

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