Sum of First 'n' Terms of an A.P.

The real power of an arithmetic progression lies in being able to add up a long list of numbers without actually adding them one by one. Instead of summing $2, 5, 8, 11, \dots$ for a hundred terms, we look for a pattern that lets us leap straight to the total. This pattern is the sum formula, and it works because the first and last terms, the second and second-last, and so on, all pair up to give the same constant sum. Once you see that symmetry, the formula $S_n = \frac{n}{2}[2a + (n-1) …