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 Arithmetic and Geometric Addle (Posted on 2014-10-10)
(A) Find two positive integers x and y, such that:
(i) y divides x, and:
(ii) x/y, x+y and x*y are in arithmetic sequence.

(B) Keeping all the other conditions in (A) unaltered, what would the value of x and y be, if clause (ii) is rewritten as:
x/y, x-y and x+y are in geometric sequence?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 3
DefDbl A-Z
Dim crlf\$

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True

DoEvents

For y = 1 To 10000
For q = 1 To 10000
x = y * q
s = x + y
prod = x * y
If s - q = prod - s Then
Text1.Text = Text1.Text & x & Str(y) & "     " & q & Str(s) & Str(prod) & crlf
DoEvents
End If
Next
Next

Text1.Text = Text1.Text & "--------------" & crlf

For y = 1 To 10000
For q = 1 To 10000
x = y * q
s = x + y
diff = x - y
If q * s = diff * diff Then
Text1.Text = Text1.Text & x & Str(y) & "     " & q & Str(diff) & Str(s) & crlf
DoEvents
End If
Next
Next

Text1.Text = Text1.Text & crlf & " done"
End Sub

finds for parts A and B, separated by a line of hyphens:

`x  y     series8  2     4 10 16---------------9  3     3 6 1212 6     2 6 18`

 Posted by Charlie on 2014-10-10 14:55:13

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