Asked by Anonymous
If (3-x) +(6)+(7-5x) is a geometric series, find two possible values for
A,x
B,the common ratio
C,the sum of the GP
A,x
B,the common ratio
C,the sum of the GP
Answers
Answered by
mathhelper
we need to have:
6/(3-x) = (7-5x)/6
(3-x)(7-5x) = 36
21 - 22x + 5x^2 - 36 = 0
5x^2 - 22x - 15 = 0
(x-5)(5x + 3) = 0
x = 5 or x = -3/5
if x = 5, the series is -2 + 6 - 18 = -14 and r = -3
if x = -3/5, the series is 18/5 + 6 + 10 = 62/3 , and r = 5/3
check my arithmetic
6/(3-x) = (7-5x)/6
(3-x)(7-5x) = 36
21 - 22x + 5x^2 - 36 = 0
5x^2 - 22x - 15 = 0
(x-5)(5x + 3) = 0
x = 5 or x = -3/5
if x = 5, the series is -2 + 6 - 18 = -14 and r = -3
if x = -3/5, the series is 18/5 + 6 + 10 = 62/3 , and r = 5/3
check my arithmetic
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