# Interesting sequence

Algebra Level 4

Let $$a_1,a_2,\ldots,a_{201}$$ be a sequence of positive integers with $$a_1=a_{201}=19999$$. It is given that every term in the sequence is less than the average of its two neighbours by a fixed positive integer $$d$$. Find the sum of all possible values of $$a_{26}$$.

×