The sum of the first $n$ terms of an AP with first term $a$ and last term $l$ is

1. NCERT §8.2 derives the AP sum. 2. Pair up terms: 1st + last = $a + l$; 2nd + second-last = $a + l$; etc. Each pair sums to $a + l$. 3. With $n$ terms, there are $n/2$ such pairs (works whether $n$ is even or odd by symmetry). 4. Sum: $S_n = (n/2)(a + l)$. 5. Equivalently, using $l = a + (n-1)d$: $S_n = (n/2)\,[2a + (n-1)d]$. 6. Example: $1 + 2 + 3 + \ldots + 100 = (100/2)(1 + 100) = 50 \cdot 101 = 5050$ ✓ (Gauss's famous childhood calculation). 7. Other options have wrong dimensions or factors. _Source: NCERT Class 11 Mathematics, Ch 8, §8.2 (AP sum formula), p. 3–4._