An arithmetic-geometric series has terms: a, (a+d)r, (a+2d)r^2, ..., [a+(n-1)d]r^(n-1). Sum technique: Let S = sum. Compute rS. Then S - rS = a + d(r+r^2+...+r^(n-1)) - [a+(n-1)d]r^n. Simplify the GP part. For infinite series (|r|<1): S = a/(1-r) + dr/(1-r)^2.