Imports System
'Pattern Explanation:
'
'The sequence is: 8, 64, 80, 136, 152
'
'Compute the differences between consecutive numbers:
'64 - 8 = 56
'80 - 64 = 16
'136 - 80 = 56
'152 - 136 = 16
'
'The pattern clearly alternates:
'+56, +16, +56, +16, ...
'
'8 + 56 = 64
'64 + 16 = 80
'80 + 56 = 136
'136 + 16 = 152
'
'This alternating pattern continues forever.
'
'Even-term formula:
'Term(2) = 64
'Each pair adds: 56 + 16 = 72
'
'Number of even terms up to Term(100):
'100 / 2 = 50 even terms
'
'Number of full pairs after Term(2):
'50 - 1 = 49 pairs
'
'Formula for even terms:
'Term(n) = 64 + 72 × (n/2 - 1)
'
'For n = 100:
'Term(100) = 64 + 72 × 49 = 3592
'
Module NextSequenceNumber
' ------------------------------------------------------------
' Function to compute the nth term using the even-term formula
' ------------------------------------------------------------
Function NthTerm(n As Integer) As Integer
If n = 1 Then
Return 8 ' first term is fixed
End If
If n Mod 2 = 0 Then
' Even term formula
Return 64 + 72 * (n \ 2 - 1)
Else
' Odd term = previous even term + 16
Dim evenTerm As Integer = 64 + 72 * ((n - 1) \ 2 - 1)
Return evenTerm + 16
End If
End Function
Sub Main()
Dim n As Integer = 100
Dim resultValue As Integer = NthTerm(n)
Console.WriteLine("The 100th term of the sequence is: " & resultValue)
End Sub
End Module
' Run:
'
' The 100th term of the sequence is: 3592
'
