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Find x so that x-2, x+2 and x+4 are consecutive terms of a geometric sequence.

 Jan 24, 2021
 #1
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Call the common ratio , r

 

(x  - 2)r  = ( x + 2)     ⇒   xr   - 2r  =   x +  2             (1)

( x +2)r  = x +  4      ⇒    xr  + 2r  =   x +  4              (2)

 

Subtract  (1)  from (2)

4r  =   2

r  = 2/4 =  1/2

 

Using the  first equation

 

x (1/2)  - 2(1/2)   = x +  2

 

(1/2)x - 1   = x +  2

 

-(1/2)x  =  3

 

x  =  3/(-1/2)    = -6

 

(x - 2)  =     -8

( x + 2)  =   -4

(x + 4)   =   -2

 

 

cool cool cool

 Jan 24, 2021

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