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[DarkDude]

If x, y, x+y are in arithmetic sequence, and x, y, 20 are in geometric sequence show that y=0 or y=10.

 

[acmilan]

x, y and x + y are in arithmetic sequence implies:

y - x = x + y - y
ie. y - x = x
x = 0.5y

x, y, 20 in geometric series implies:

y/x = 20/y

y² = 20x

but we know x = 0.5y, so:

y² = 10y

y² - 10y = 0
y(y - 10) = 0

Hence y = 0 or y = 10

 

[DarkDude]

Thanks so much acmilan