Find the sum of the first 10 multiples of 2.

Answer

To find the sum of the first 10 multiples of 2, we can follow these steps:

### Step 1: Identify the first 10 multiples of 2
The first 10 multiples of 2 are:
1. 2 × 1 = 2
2. 2 × 2 = 4
3. 2 × 3 = 6
4. 2 × 4 = 8
5. 2 × 5 = 10
6. 2 × 6 = 12
7. 2 × 7 = 14
8. 2 × 8 = 16
9. 2 × 9 = 18
10. 2 × 10 = 20

So, the first 10 multiples of 2 are: **2, 4, 6, 8, 10, 12, 14, 16, 18, 20**.

### Step 2: Write down the series
The series can be written as:
\[ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 \]

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

### Step 4: Substitute the values into the formula
In our case:
- \( n = 10 \) (the number of terms)
- \( a = 2 \) (the first term)
- \( l = 20 \) (the last term)

Now, substituting these values into the formula:
\[ S_{10} = \frac{10}{2} \times (2 + 20) \]

### Step 5: Calculate the sum
Calculating the expression:
\[ S_{10} = 5 \times (2 + 20) \]
\[ S_{10} = 5 \times 22 \]
\[ S_{10} = 110 \]

### Final Answer
The sum of the first 10 multiples of 2 is **110**.

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