The sum of first 30 even natural numbers is

Options

A. 930
B. 950
C. 910
D. 980

Answer

To find the sum of the first 30 even natural numbers, we can follow these steps:

### Step 1: Identify the first 30 even natural numbers
The first 30 even natural numbers are:
2, 4, 6, 8, ..., 60.

### Step 2: Recognize that this is an Arithmetic Progression (AP)
The sequence of even numbers forms an arithmetic progression (AP) where:
- The first term (a) = 2
- The common difference (d) = 2
- The number of terms (n) = 30

### Step 3: Use the formula for the sum of an AP
The sum \( S_n \) of the first n terms of an arithmetic progression can be calculated using the formula:
\[ S_n = \frac{n}{2} \times (2a + (n - 1)d) \]
where:
- \( n \) = number of terms
- \( a \) = first term
- \( d \) = common difference

### Step 4: Substitute the values into the formula
Substituting the known values into the formula:
\[ S_{30} = \frac{30}{2} \times (2 \times 2 + (30 - 1) \times 2) \]

### Step 5: Simplify the expression
Calculating step-by-step:
1. Calculate \( \frac{30}{2} = 15 \)
2. Calculate \( 2 \times 2 = 4 \)
3. Calculate \( (30 - 1) \times 2 = 29 \times 2 = 58 \)
4. Now substitute these values back:
\[ S_{30} = 15 \times (4 + 58) \]
5. Calculate \( 4 + 58 = 62 \)
6. Finally, calculate \( 15 \times 62 \):
\[ S_{30} = 930 \]

### Conclusion
The sum of the first 30 even natural numbers is **930**.

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