# SOLUTION: the second term of the infinite geometric series, a + ar + ar^2 + ar^3...... is eaqual to 4 and the same to infinity of this series is 18. Find the two possible values of th

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 Question 193885: the second term of the infinite geometric series, a + ar + ar^2 + ar^3...... is eaqual to 4 and the same to infinity of this series is 18. Find the two possible values of the common ratio, r. what are the corresponding values of a? Found 2 solutions by radikrr, stanbon:Answer by radikrr(7)   (Show Source): You can put this solution on YOUR website! ar=4 a/(1-r)=18 a=4/r 4/r=(1-r)18 4/r=(1-r)18 2/9=(1-r)r r^2-r+2/9=0 D = 1-8/9=1/9 r1=2/3 r2=1/3 a1=6 a2=18 Answer by stanbon(69061)   (Show Source): You can put this solution on YOUR website! the second term of the infinite geometric series, a + ar + ar^2 + ar^3...... is equal to 4 and the same to infinity of this series is 18. Find the two possible values of the common ratio, r. what are the corresponding values of a? ---------------- 2nd term: a(2) = ar = 4 Sum : a/(1-r) = 18 -------------------------- Rearrange: a = 4/r --- Substitute: (4/r)/(1-r) = 18 4/r = 18 - 18r 4 = 18r-18r^2 18r^2 - 18r +4 = 0 9r^2 - 9r + 2 = 0 9r^2 - 6r - 3r + 2 = 0 3r(3r-2)-(3r-2) = 0 (3r-2)(3r-1) = 0 r = 2/3 or r = 1/3 ------------- Since a = 4/r a = 6 when r = 2/3 or a = 12 when r = 1/3 --------------------- Cheers, Stan H