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Author: CodewithAsh10

Seqence_Number.py

@@ -0,0 +1,114 @@
+def arithmetic_sequence (a1 , d , n):
+    return [ a1 + (i - 1) * d for i in range (1 , n + 1) ]
+a1 = 3 # first term
+d = 4 # common difference
+n = 5 # number of terms
+arithmetic_seq = arithmetic_sequence (a1 , d , n)
+print (" Arithmetic Sequence :", arithmetic_seq )
+
+#******************************************************************************
+def geometric_sequence ( a1 , r , n):
+    return [ a1 * (r ** (i - 1) ) for i in range (1 , n + 1) ]
+a1 = 2 # first term
+r = 3 # common ratio
+n = 4 # number of terms
+geometric_seq = geometric_sequence ( a1 , r , n)
+print (" Geometric Sequence :", geometric_seq )
+
+#******************************************************************************
+def fibonacci_sequence ( n):
+    fib_seq = [0 , 1]
+    for i in range (2 , n ):
+        fib_seq . append ( fib_seq [ -1] + fib_seq [ -2])
+    return fib_seq [: n]
+n = 10 # number of terms
+fibonacci_seq = fibonacci_sequence ( n)
+print (" Fibonacci Sequence :", fibonacci_seq )
+
+#******************************************************************************
+
+def harmonic_sequence (n ):
+    return [1 / i for i in range (1 , n + 1) ]
+n = 5 # number of terms
+harmonic_seq = harmonic_sequence (n)
+print (" Harmonic Sequence :", harmonic_seq )
+
+#******************************************************************************
+def square_numbers (n):
+    return [i **2 for i in range (1 , n + 1) ]
+n = 5 # number of terms
+square_seq = square_numbers (n)
+print (" Square Numbers :", square_seq )
+
+#******************************************************************************
+
+def cube_numbers (n ):
+    return [i **3 for i in range (1 , n + 1) ]
+n = 5 # number of terms
+cube_seq = cube_numbers (n )
+print (" Cube Numbers :", cube_seq )
+
+#******************************************************************************
+def triangular_numbers ( n):
+    return [i * (i + 1) // 2 for i in range (1 , n + 1) ]
+n = 5 # number of terms
+triangular_seq = triangular_numbers (n)
+print (" Triangular Numbers :", triangular_seq )
+
+#******************************************************************************
+
+def is_prime ( num ):
+    if num <= 1:
+        return False
+    for i in range (2 , int ( num **0.5) + 1) :
+        if num % i == 0:
+            return False
+        return True
+def prime_numbers ( n):
+    primes = []
+    num = 2
+    while len ( primes ) < n:
+        if is_prime ( num ):
+            primes . append ( num )
+        num += 1
+    return primes
+n = 6 # number of terms
+prime_seq = prime_numbers ( n)
+print (" Prime Numbers :", prime_seq )
+
+#******************************************************************************
+
+def factorial_sequence ( n):
+    factorials = [1]
+    for i in range (1 , n + 1) :
+        factorials . append ( factorials [ -1] * i)
+    return factorials
+n = 5 # number of terms
+factorial_seq = factorial_sequence ( n)
+print (" Factorial Sequence :", factorial_seq )
+
+#******************************************************************************
+
+def alternating_sequence (n):
+    return [( -1) ** i for i in range (n) ]
+n = 10 # number of terms
+alternating_seq = alternating_sequence ( n)
+print (" Alternating Sequence :", alternating_seq )
+
+#******************************************************************************
+
+def exponential_sequence (b , n):
+    return [b ** i for i in range (1 , n + 1) ]
+b = 2 # base
+n = 5 # number of terms
+exponential_seq = exponential_sequence (b , n )
+print (" Exponential Sequence :", exponential_seq )
+
+#******************************************************************************
+
+from math import comb
+def catalan_numbers (n):
+    return [ comb (2 * i , i) // ( i + 1) for i in range (n) ]
+n = 5 # number of terms
+catalan_seq = catalan_numbers (n)
+print (" Catalan Numbers :", catalan_seq )