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Sum of terms of a sequence

Source: 1959 AHSME Problem 39

August 14, 2013
geometric seriesAMC

Problem Statement

Let SS be the sum of the first nine terms of the sequence x+a,x2+2a,x3+3a,⋯ .x+a, x^2+2a, x^3+3a, \cdots. Then SS equals: <spanclass=′latex−bold′>(A)</span> 50a+x+x8x+1<spanclass=′latex−bold′>(B)</span> 50a−x+x10x−1<spanclass=′latex−bold′>(C)</span> x9−1x+1+45a <span class='latex-bold'>(A)</span>\ \frac{50a+x+x^8}{x+1} \qquad<span class='latex-bold'>(B)</span>\ 50a-\frac{x+x^{10}}{x-1}\qquad<span class='latex-bold'>(C)</span>\ \frac{x^9-1}{x+1}+45a\qquad<spanclass=′latex−bold′>(D)</span> x10−xx−1+45a<spanclass=′latex−bold′>(E)</span> x11−xx−1+45a<span class='latex-bold'>(D)</span>\ \frac{x^{10}-x}{x-1}+45a\qquad<span class='latex-bold'>(E)</span>\ \frac{x^{11}-x}{x-1}+45a
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