# Answer to Question #23085 in Algebra for Karen

Question #23085

Which of the following values of x will make the sequence 3x, 4x+2, 7x-1 a geometric sequence?

Expert's answer

if 3x, 4x+2, 7x-1 is geometric sequence then

3x/(4x+2)=(4x+2)/(7x-1)3x(7x-1)=(4x+2)^2

21x^2-3x=16x^2+16x+4

5x^2-19x-4=0

D=19^2+4*5*4=361+80=441=(21)^2

so x1,2=( 19+-21)/10

so x1=4 and x2=-0.2

so only for these values we get geometric sequence

3x/(4x+2)=(4x+2)/(7x-1)3x(7x-1)=(4x+2)^2

21x^2-3x=16x^2+16x+4

5x^2-19x-4=0

D=19^2+4*5*4=361+80=441=(21)^2

so x1,2=( 19+-21)/10

so x1=4 and x2=-0.2

so only for these values we get geometric sequence

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## Comments

Assignment Expert29.01.13, 15:48You're welcome! We are glad to be helpful.

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Karen29.01.13, 15:45Ohhhhh thanks btw :)))

Assignment Expert29.01.13, 15:43Dear visitor

The formula used in solution follows from basic properties of geometric sequence. As we know, general form of geometric sequence is a, ar, ar^2, ar^3,...

So a1=a

a2=ar

a3=ar^2

Therefore a1/a2=a/ar=1/r

a2/a3=ar/ar^2=1/r

whence a1/a2=a2/a3

Karen29.01.13, 15:30Umm hello could you explain it more detailed?? I wanted to know how it come up with that formula and answer. If that would be okay? Thanks :)

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