1975 AMC 12 Question 9

Let $a_1,$ $a_2,$ $\ldots$ and $b_1,$ $b_2,$ $\ldots$ be arithmetic progressions such that $a_1=25,$ $b_1=75,$ and $a_{100}+b_{100}=100.$ Find the sum of the first one hundred terms of the progression $a_1+b_1,$ $a_2+b_2,$ $\ldots.$