MathDB
First term of an infinite geometric series

Source: 1970 AHSME Problem 19

March 24, 2014
ratiogeometric seriesAMC

Problem Statement

The sum of an infinite geometric series with common ratio rr such that r<1|r|<1, is 1515, and the sum of the squares of the terms of this series is 4545. The first term of the series is
<spanclass=latexbold>(A)</span>12<spanclass=latexbold>(B)</span>10<spanclass=latexbold>(C)</span>5<spanclass=latexbold>(D)</span>3<spanclass=latexbold>(E)</span>2<span class='latex-bold'>(A) </span>12\qquad<span class='latex-bold'>(B) </span>10\qquad<span class='latex-bold'>(C) </span>5\qquad<span class='latex-bold'>(D) </span>3\qquad <span class='latex-bold'>(E) </span>2