# Two arithmetic sequences, with a twist

Algebra Level 4

Given that we have two arithmetic sequences $$\{a_n\}, \{b_n\}$$ where

$$a_1 = 9$$, $$a_{n+1} - a_n = 3$$ for all natural $$n$$

$$b_1 = 0$$, $$b_{n+1} - b_n = 5$$ for all natural $$n$$

Now, find the smallest possible sum of the first $$x$$ terms of the sequence $$\{a_n\}$$ and the first $$y$$ terms of the sequence $$\{b_n\}$$ given that $$x+y = 10$$, and $$x,y$$ are natural numbers.

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