The sum of the first $n$ terms of a GP with first term $a$ and common ratio $r \neq 1$ is

1. NCERT §8.3 derives the GP sum. 2. Write: $S_n = a + ar + ar^2 + \ldots + ar^{n-1}$. 3. Multiply both sides by $r$: $r S_n = ar + ar^2 + \ldots + ar^n$. 4. Subtract: $S_n - r S_n = a - a r^n$, so $S_n (1 - r) = a(1 - r^n)$. 5. Solve: $S_n = \dfrac{a(1 - r^n)}{1 - r} = \dfrac{a(r^n - 1)}{r - 1}$. Same formula written two ways. 6. Option B is wrong (binomial-style). Option C is the AP product. Option D is the INFINITE GP sum (only when $|r| < 1$). _Source: NCERT Class 11 Mathematics, Ch 8, §8.3 (GP sum), p. 6–7._