Find the sum of first 10 multiples of 6.

Answer

To find the sum of the first 10 multiples of 6, we can follow these steps:

### Step 1: Identify the first 10 multiples of 6
The first 10 multiples of 6 can be calculated by multiplying 6 with the first 10 natural numbers:
- 1 × 6 = 6
- 2 × 6 = 12
- 3 × 6 = 18
- 4 × 6 = 24
- 5 × 6 = 30
- 6 × 6 = 36
- 7 × 6 = 42
- 8 × 6 = 48
- 9 × 6 = 54
- 10 × 6 = 60

Thus, the first 10 multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

### Step 2: Write down the series
The series of the first 10 multiples of 6 is:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

### Step 3: Identify the first term (A), last term (AN), and number of terms (N)
- First term (A) = 6
- Last term (AN) = 60
- Number of terms (N) = 10

### Step 4: Use the formula for the sum of an arithmetic series
The formula for the sum \( S_n \) of the first \( n \) terms of an arithmetic series is:
\[ S_n = \frac{n}{2} \times (A + AN) \]
Substituting the values we have:
\[ S_{10} = \frac{10}{2} \times (6 + 60) \]

### Step 5: Calculate the sum
Calculating inside the parentheses:
\[ 6 + 60 = 66 \]
Now substituting back into the formula:
\[ S_{10} = 5 \times 66 = 330 \]

### Final Answer
The sum of the first 10 multiples of 6 is **330**.

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