Question

2 + 4 + 6 +............100 =

• A. 2550
• B. 2505
• C. 2560
• D. 2530

Answer 1

Answer:

A. 2550

There are two simple ways to solve this sum:

Method 1: Formula for Sum of First $n$ Even Numbers

The formula to find the sum of the first $n$ even numbers is $n(n + 1)$.

• In the series $2 + 4 + 6 + \dots + 100$, there are 50 even numbers ($n = 50$).

• Sum = $50 \times (50 + 1)$

• Sum = $50 \times 51 = \mathbf{2550}$

---

Method 2: Arithmetic Progression (AP) Formula

In this series:

• First term ($a$) = 2

• Last term ($l$) = 100

• Number of terms ($n$) = 50

The formula for the sum is: $S_n = \frac{n}{2} (a + l)$

• $S_{50} = \frac{50}{2} (2 + 100)$

• $S_{50} = 25 \times 102 = \mathbf{2550}$

Therefore, $2 + 4 + 6 + \dots + 100 = 2550$.