How do I find the sum of the first n terms of an AP without adding them one by one?

Use the sum formula Sₙ = n/2 [2a + (n − 1)d], where a is the first term, d is the common difference, and n is the number of terms. For 2, 5, 8..., here a = 2 and d = 3. To find the sum of the first 20 terms, put n = 20: S₂₀ = 20/2 [2×2 + (20 − 1)×3] = 10 [4 + 57] = 10 × 61 = 610. If instead you know the last term l, you can use the shorter form Sₙ = n/2 (a + l), which is just the average of the first and last term times the number of terms. Pick whichever form matches the information given in the problem.