Graduate Management Admission Test (GMAT) Practice Test

To find the sum of a sequence of consecutive or evenly spaced integers, what is the calculation required?

1. Multiply the number of terms by the smallest integer

2. Multiply the average of the largest and smallest term by the number of terms

3. Sum all individual terms in the sequence

4. Calculate the median of the sequence

The correct answer is: Multiply the average of the largest and smallest term by the number of terms

The calculation to find the sum of a sequence of consecutive or evenly spaced integers involves determining the average of the largest and smallest terms and then multiplying that average by the total number of terms in the sequence. This method is rooted in the concept of an arithmetic series. When you have consecutive integers, they form a linear sequence where the smallest term and the largest term help define the average. The average can be thought of as the midpoint of the range of integers. By multiplying this average by the number of terms, you effectively calculate the total of all terms in the sequence. This approach is efficient because it leverages the properties of symmetry in evenly spaced numbers, ensuring that all terms are represented in the calculation without the need for individually summing each term, which can be cumbersome. Other methods, such as summing individual terms directly, can be time-consuming, especially for long sequences. Therefore, using the average method provides a clear and simplified pathway to arrive at the correct total for the sum of the sequence.