Ace the BMAT 2025 – Unleash Your Biomedical Superpowers!

The formula for the sum of the first n terms of an arithmetic series is correctly represented by the statement that involves the average of the first and last terms multiplied by the number of terms. When you have an arithmetic series, the terms are evenly spaced, and the sum can be efficiently calculated by considering the average of the first term and the last term.

In an arithmetic series, the first term is denoted as 'a' and the last term can be found by the formula for the nth term, which is 'a + (n-1)d', where 'd' is the common difference between successive terms. Therefore, the last term can be expressed in relation to the first term, which when added to the first term gives the total sum of the first and last terms.

By finding the average of the first and last term, you have (first + last)/2. The sum of n terms is then this average times the number of terms n, giving you the formula Sn = n × (first + last)/2. This method is effective because it leverages the symmetrical properties of the arithmetic sequence, leading to a straightforward calculation of the sum.

This formula works well regardless of how large n is and is a key part of understanding