What is the sum of the first 5 numbers in this series: 2, 4, 6, 8, 10?

The given series is: 2, 4, 6, 8, 10.

These are the first 5 terms of an arithmetic sequence where the first term (\(a_1\)) is 2 and the common difference (\(d\)) is 2.

To find the sum of the first 5 terms, use the formula for the sum of an arithmetic series:

\[
S_n = \frac{n}{2} \times (a_1 + a_n)
\]

Where:
- \(n\) is the number of terms
- \(a_1\) is the first term
- \(a_n\) is the nth term (in this case, the 5th term)

Plugging in the values:

\[
S_5 = \frac{5}{2} \times (2 + 10)
\]

\[
S_5 = \frac{5}{2} \times 12 = 5 \times 6 = 30
\]

So, the sum of the first 5 numbers in the series is **30**.

Would you like to go over the steps in more detail or have any other questions?

Here are 5 related questions you might be interested in:
1. What is the sum of the first 10 terms of this series?
2. How do you find the common difference in an arithmetic sequence?
3. What is the formula for the sum of an arithmetic series with more than 5 terms?
4. How do you find the nth term in an arithmetic sequence?
5. Can the sum of a series be calculated using a different method?

**Tip:** When working with arithmetic series, always identify the first term and the common difference before applying any formulas.

Learn how to calculate the sum of the first 5 numbers in the arithmetic sequence 2, 4, 6, 8, 10 using the formula for the sum of an arithmetic series. This problem covers key mathematical concepts including arithmetic sequences and series sums. Suitable for students in Grades 7-9.

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