An arithmetic sequence has the recursive structure
\(a_n=a_{n-1}+d\)
and can be solved explicitly for the \(n\) term, \(a_n\), in terms of the first term of the sequence \(a_1\).
\(a_n=a_{n-1}+d\)
\(\implies~a_n=a_{n-2}+2d\)
\(\implies~a_n=a_{n-3}+3d\)
\(\implies\cdots\implies a_n=a_1+(n-1)d\)
You know the 100th term of the sequence is \(a_{100}=1000\) and that the common difference between terms is \(d=5\), which means you have enough information to find the first term:
\(a_{100}=a_1+(100-1)\times5\implies1000=a_1+99\times5\implies a_1=505\)
