Question 4Let $a_1,a_2,\ldots$ and $b_1,b_2,\ldots$ be two arithmetic progressions such that $a_1=10$ and $b_1=24$, and that $a_{100}+b_{100}=2014$. Find the sum of the first twenty terms of the sequence $$a_1+b_1,a_2+b_2,a_3+b_3,\ldots.$$