 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Seventh Term Settlement (Posted on 2016-07-22) Each of A(1), A(2),..., A(7) is a positive integer such that:

(i) A(6) = 144, and

(ii) A(n+3) = A(n+2)(A(n+1)+A(n)), for n = 1,2,3,4

Find A(7)

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer solution | Comment 2 of 10 | First let's make (ii) more manageable by writing the recursion in more usual terms:

A(n) = A(n-1)*(A(n-2) + A(n-3)) for n = 4, 5, 6 and 7

DefDbl A-Z
Dim crlf\$, a(7)

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For a1 = 1 To 36
a(1) = a1
For a2 = 1 To 36
a(2) = a2
For a3 = 1 To 36
DoEvents
a(3) = a3
For i = 4 To 7
a(i) = a(i - 1) * (a(i - 2) + a(i - 3))
Next i
If a(6) = 144 Then
For i = 1 To 7
Text1.Text = Text1.Text & Str(a(i))
Next i
Text1.Text = Text1.Text & crlf
End If
Next
Next
Next
Text1.Text = Text1.Text & crlf & " done"

End Sub

resulting in:

2 1 2 6 18 144 3456
7 1 1 8 16 144 3456

The results show that A(6) is 144 only if A(1), A(2) and A(3) are either 2, 1 and 2; or 7, 1 and 1, respectively.  Either way A(7) is 3456.

 Posted by Charlie on 2016-07-22 10:34:02 Please log in:

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