Final answer:
In mathematics, a for loop can be used to sum a series of numbers by initializing a total variable, iterating through each number, adding each to the total, and obtaining the sum of all numbers after the loop completes.
Step-by-step explanation:
In mathematics, the symbol Σ, pronounced 'sigma', is used to denote the sum of a series of numbers. When you see an expression that includes Σ, it means that you are to perform an addition of a sequence of terms. Using a for loop in programming is one method to automate this process. For instance, if you were to write a for loop to sum the sequence of numbers given in an array, your algorithm would initialize a total variable at zero, iterate through the array adding each number to the total, and at the end of the loop, you would have the sum of all numbers in the array.
To illustrate, let's consider the specific example where you want to compute the sum of the following set of data values: 0, 5, 5, 15, 30, 30, 45, 50, 50, 60, 75, 110, 140, 240, 330:
- Initialize a total sum variable to 0.
- Use a for loop to go through each data value in the set.
- Add each value to the total sum within the for loop.
- After the loop has finished, the total sum variable will contain the sum of all the data values.