Ace the BMAT 2025 – Unleash Your Biomedical Superpowers!

In an arithmetic sequence, each term is generated by adding a constant value, known as the common difference, to the previous term. The first term of the sequence is denoted as \( a \), and the common difference is denoted as \( d \).

To derive the formula for the nth term, consider the sequence:

1. The first term (n = 1) is simply \( a \).

2. The second term (n = 2) is \( a + d \).

3. The third term (n = 3) is \( a + 2d \).

4. Continuing this pattern, the nth term can be expressed as adding \( d \) a total of \( n - 1 \) times to the first term \( a \).

Thus, the general formula for the nth term \( a_n \) of the sequence is expressed mathematically as:

\[ a_n = a + (n - 1)d \]

This formula precisely captures how each term in the sequence relates to the initial term and how many times the common difference has been added based on the position of that term in the sequence.

Therefore, the correct expression for the nth term in an arithmetic series is indeed \( a + (