perplexus.info :: Sequences : Arithmetic and Geometric Addle

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?

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

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

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

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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