For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. For example, in the sequence 2, 5, 8, 11, the common difference is 3. Understanding this concept is crucial for identifying the first three terms and the last term in the given problem.

Summation notation, represented by the sigma symbol (Σ), is a concise way to express the sum of a sequence of terms. In the given problem, Σ from i=1 to 100 of 4i indicates that we are summing the values of 4i for each integer i from 1 to 100. This notation is essential for understanding how to calculate the total sum of the specified terms.

The formula for the sum of the first n terms of an arithmetic sequence is S_n = n/2 * (a + l), where S_n is the sum, n is the number of terms, a is the first term, and l is the last term. This formula allows for efficient calculation of the total sum without needing to add each term individually. Applying this formula is key to solving the problem presented.