Arithmetic progression nth term – UGC NET Question

This option is correct because the standard formula for the nth term of an arithmetic progression is aₙ = a + (n−1)d. Here, a is the first term and d is the constant difference between successive terms. This formula comes from adding the common difference repeatedly. Therefore, the nth term is a + (n−1)d.

Option A:
The expression a + nd adds the common difference n times, which overshoots by one step. It would correctly represent the (n+1)th term, not the nth term. Hence, this option is not correct.

Option B:
The expression a − (n−1)d would produce a decreasing sequence even if d is positive. It does not match the usual pattern for an arithmetic progression defined by adding d each time. Therefore, this option is not suitable.

Option C:
The expression nd ignores the first term a entirely and cannot generate the correct sequence unless a is zero. It fails to describe the general nth term formula. Thus, this option is incorrect.

Option D:
The formula a + (n−1)d starts from a and adds the common difference d exactly n−1 times. This accurately generates each term of the progression in order, making it the correct general term.