1955 AHSME Problem 45

Given a geometric sequence with the first term \neq 0 and r \neq 0 and an arithmetic sequence with the first term =0. A third sequence 1,1,2\ldots is formed by adding corresponding terms of the two given sequences. The sum of the first ten terms of the third sequence is:

\begin{array}{l} \textbf{(A)}\ 978\qquad\textbf{(B)}\ 557\qquad\textbf{(C)}\ 467\qquad\textbf{(D)}\ 1068\\ \textbf{(E)}\ \text{not possible to determine from the information given} \end{array}

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