V. b. Suppose that {a} is a sequence of real numbers defined recursively bya₁ = 1, a₂ = 2, and an+2C.=an+¹ n Write out the first 13 terms and give a closed form formula for aanLet P(n):9+13+...+(4n+5) =4n² +14n+12Show P(k) ⇒ P(k+1). Does this mean P(n) is true Vintegers n≥1?

note :Since you have posted multiple questions, we will provide the solution only to the first question as per our Q&A guidelines. Please repost the remaining questions separately.As per the question we are given a sequence and we have to calculate it's first terms..1import sympy as sp 2 3# Define the recursive sequence 4def recursive_sequence(n, sequence): 5 if n < len(sequence): 6 return sequence[n-1] 7 else: 8 # Calculate the next term using the recursive formula 9 next_term = sequence[-2] / sequence[-1] 10 sequence.append(next_term) 11 return recursive_sequence(n, sequence) 12 13# Initial terms 14sequence = [1, 2] 15# Calculate the first 13 terms 16first_13_terms = [recursive_sequence(n, sequence) for n in range(1, 14)] 17 18first_13_terms 19The code first defined a function `recursive_sequence` to generate terms of the sequence based on the recursive definition given:- - - The function checks if the requested term is already in the list of known terms. If it is, it returns the term. If not, it calculates the next term using the recursive relationship, appends it to the sequence, and calls itself again until the requested term is computed.Next, we initialized the sequence with its first two terms, 1 and 2, and generated the first 13 terms by calling the `recursive_sequence` function for each term from 1 to 13.The attempt to find a closed-form solution involved looking for a pattern in the terms, specifically identifying indices where the terms are powers of 2 or their inverses.Code Output :[1, 2, 0.5, 4.0, 0.125, 32.0, 0.00390625, 8192.0, 4.76837158203125e-07, 17179869184.0, 2.7755575615628914e-17, 6.189700196426902e+26, 4.484155085839415e-44]