The $n^\text{th}$ term of a Geometric Progression (GP) with first term $a$ and common ratio $r$ is

1. NCERT §8.3 (Geometric Progression): each term is obtained by MULTIPLYING the previous term by the common ratio $r$. 2. Terms: $a_1 = a$, $a_2 = ar$, $a_3 = ar^2$, $\ldots$ 3. Pattern: the $n^\text{th}$ term has $(n-1)$ multiplications by $r$, so $a_n = a r^{n-1}$. 4. Example: GP $2, 6, 18, 54, \ldots$ with $a = 2$, $r = 3$. The 4th term: $a_4 = 2 \cdot 3^{4-1} = 2 \cdot 27 = 54$ ✓. 5. Option B uses wrong exponent. Option C is the AP formula. Option D has wrong functional form. _Source: NCERT Class 11 Mathematics, Ch 8, §8.3 (Geometric Progression), p. 5._