Which of the following values of x will make the sequence 3x, 4x+2, 7x-1 a geometric sequence?
1
Expert's answer
2013-01-29T08:27:14-0500
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
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Karen
29.01.13, 15:45
Ohhhhh thanks btw :)))
Assignment Expert
29.01.13, 15:43
Dear 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
Karen
29.01.13, 15:30
Umm 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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You're welcome! We are glad to be helpful. If you really liked our service please press like-button beside answer field. Thank you!
Ohhhhh thanks btw :)))
Dear 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
Umm 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 :)
Leave a comment