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Arithmetic and Geometric Addle (Posted on 2014-10-10) Difficulty: 3 of 5
(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    
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Solution computer solution | Comment 1 of 3
DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 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     series
8  2     4 10 16
---------------
9  3     3 6 12
12 6     2 6 18

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