Question 8
For any sequence of real numbers $A=(a_1,a_2,a_3,\ldots),$ define $\Delta A$ to be the sequence $(a_2-a_1,a_3-a_2,a_4-a_3,\ldots),$ whose $n$th term is $a_{n+1}-a_n.$ Suppose that all of the terms of the sequence $\Delta(\Delta A)$ are $1,$ and that $a_{19}=a_{92}=0.$ Find $a_1.$