Write an algorithm to obtain the sum of the first ten terms of the sequence using recursion. Also give iterative algorithm.

Recursive Algorithm:

1. Define a recursive function sum_of_terms(n) that takes an integer n as input and returns the sum of the first n terms of the sequence.
2. In the base case, when n is equal to 1, return 1. This is because the sum of the first term of the sequence is simply the first term itself.
3. In the recursive case, when n is greater than 1, calculate the sum of the first n-1 terms of the sequence using the recursive call sum_of_terms(n-1). Then, add the n-th term of the sequence to this sum and return the result.

Here is the recursive algorithm in Python:

def sum_of_terms(n):
  """
  Calculates the sum of the first n terms of the sequence.

  Args:
    n: The number of terms to sum.

  Returns:
    The sum of the first n terms of the sequence.
  """

  # Base case: When n is equal to 1, return 1.
  if n == 1:
    return 1

  # Recursive case: When n is greater than 1, calculate the sum of the first n-1 terms of the sequence
  # using the recursive call sum_of_terms(n-1). Then, add the n-th term of the sequence to this sum and
  # return the result.
  else:
    return sum_of_terms(n-1) + n

Iterative Algorithm:

1. Initialize a variable sum to 0. This variable will store the sum of the first n terms of the sequence.
2. Initialize a variable term to 1. This variable will store the current term of the sequence.
3. Iterate over the numbers from 1 to n.
4. In each iteration, add the current term to the sum.
5. Calculate the next term in the sequence by adding 1 to the current term.
6. Repeat steps 3-5 until all the terms from 1 to n have been processed.

Here is the iterative algorithm in Python:

def sum_of_terms(n):
  """
  Calculates the sum of the first n terms of the sequence.

  Args:
    n: The number of terms to sum.

  Returns:
    The sum of the first n terms of the sequence.
  """

  # Initialize the sum and the current term.
  sum = 0
  term = 1

  # Iterate over the numbers from 1 to n.
  for i in range(1, n+1):
    # Add the current term to the sum.
    sum += term

    # Calculate the next term in the sequence.
    term += 1

  # Return the sum of the first n terms of the sequence.
  return sum