The $n^\text{th}$ term of an Arithmetic Progression (AP) with first term $a$ and common difference $d$ is

1. NCERT §8.2 (Arithmetic Progression): each term is obtained by adding the common difference $d$ to the previous term. 2. Terms: $a_1 = a$, $a_2 = a + d$, $a_3 = a + 2d$, $\ldots$ 3. Pattern: the $n^\text{th}$ term has $(n-1)$ additions of $d$, so $a_n = a + (n-1)d$. 4. Example: AP $3, 7, 11, 15, \ldots$ with $a = 3$ and $d = 4$. The 5th term: $a_5 = 3 + (5-1)(4) = 3 + 16 = 19$. ✓ 5. Options B and C have wrong functional forms. Option D divides instead of multiplying. _Source: NCERT Class 11 Mathematics, Ch 8 "Sequences and Series", §8.2 (Arithmetic Progression), p. 2–3._