Sequences and series problem
If x-2, x 4, 5x 2 are three consectutive terms in a geomtric sequence, determine the numerical value(s) of the common raito(s).
Solution: 3,-1
Please show some work. Thank you.
Update:thanks man
If x-2, x 4, 5x 2 are three consectutive terms in a geomtric sequence, determine the numerical value(s) of the common raito(s).
Solution: 3,-1
Please show some work. Thank you.
Update:thanks man
Comments
that's x+4 and 5x+2? your plus signs don't show.
(x+4) / (x-2) = r = (5x+2)/(x+4)
(x+4)² = (x-2)(5x+2)
x² + 8x + 16 = 5x² - 8x - 4
0 = 4x² - 16x - 20
x² - 4x - 5 = 0
(x - 5)(x + 1) = 0
x = 5 or x = -1
so r = (5+4)/(5-2) = 3 = (25+2)/(5+4),
or r = (-1+4)/(-1-2) = -1 = (-5+2)/(-1+4)