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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#340153 on Dec 2023
#340153 on Dec 2023
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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 :)