Mathematics

An arithmetic progression builds by adding the same constant amount each time, so every term follows a predictable formula. The key insight is that the $n$-th term depends linearly on the first term and the common difference: $a_n = a_1 + (n-1)d$. You know the 50th term and the common difference, so you can rearrange this formula to isolate $a_1$ and solve directly.

An arithmetic progression builds by adding the same constant amount each time, so every term follows a predictable formula. The key insight is that the $n$-th term depends linearly on the first term and the common difference: $a_n = a_1 + (n-1)d$. You know the 50th term and the common difference, so you can rearrange this formula to isolate $a_1$ and solve directly.