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1959 AMC 12 Question 39

AMC12 · 1959 AMC 12

Question 39

Let $S$ be the sum of the first nine terms of the sequence

$$
\begin{gathered} x+a,\quad x^2+2a,\\ x^3+3a,\quad\ldots. \end{gathered}
$$

Then $S$ equals:
  1. $\dfrac{50a+x+x^8}{x+1}$
  2. $50a-\dfrac{x+x^{10}}{x-1}$
  3. $\dfrac{x^9-1}{x+1}+45a$
  4. $\dfrac{x^{10}-x}{x-1}+45a$
  5. $\dfrac{x^{11}-x}{x-1}+45a$