1992 AHSME Problem 21

For a finite sequence A=(a_1,a_2,...,a_n) of numbers, the *Cesáro sum* of A is defined to be \frac{S_1+\cdots+S_n}{n} , where S_k=a_1+\cdots+a_k and 1\leq k\leq n. If the Cesáro sum of the 99-term sequence (a_1,...,a_{99}) is 1000, what is the Cesáro sum of the 100-term sequence (1,a_1,...,a_{99})?

\text{(A) } 991\quad \text{(B) } 999\quad \text{(C) } 1000\quad \text{(D) } 1001\quad \text{(E) } 1009

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.