Find the sum of all even numbers between 1 and 31.

Given data

• Even numbers between 1 and 31: 2, 4, 6, …, 30 (an AP with d = 2).

Concept / Approach

• Sum of AP: S = n/2 · (first + last).

Step-by-step calculation

a = 2, l = 30, d = 2n = ((l − a)/d) + 1 = ((30 − 2)/2) + 1 = 15S = 15/2 · (2 + 30) = 15/2 · 32 = 15 · 16 = 240

Common pitfalls

• Including 32 or excluding 2—stick to 2 through 30 inclusive.

Final Answer

Sum = 240.