This is an arithmetic sequence where the first term \( a_1 = 2 \), the common difference \( d = 2 \), and the last term \( a_n = 70 \). To find the sum of the sequence, we need to use the formula for the sum of an arithmetic series:

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

### Step 1: Find \( n \)
The number of terms \( n \) in the sequence can be found using the formula for the nth term of an arithmetic sequence:

\[
a_n = a_1 + (n - 1) \times d
\]

Substitute \( a_n = 70 \), \( a_1 = 2 \), and \( d = 2 \):

\[
70 = 2 + (n - 1) \times 2
\]

Simplifying:

\[
70 = 2 + 2n - 2
\]
\[
70 = 2n
\]
\[
n = \frac{70}{2} = 35
\]

So, there are 35 terms in the sequence.

### Step 2: Find the sum
Now, use the sum formula with \( n = 35 \), \( a_1 = 2 \), and \( a_n = 70 \):

\[
S_{35} = \frac{35}{2} \times (2 + 70)
\]
\[
S_{35} = \frac{35}{2} \times 72
\]
\[
S_{35} = 35 \times 36
\]
\[
S_{35} = 1260
\]

### Final Answer:
The sum of the sequence \( 2 + 4 + 6 + \dots + 70 \) is \( 1260 \).

Would you like more details or have any questions?

---

Here are 5 related questions:
1. What is the sum of the sequence \( 3 + 6 + 9 + \dots + 60 \)?
2. How do you find the sum of an arithmetic series where the difference is negative?
3. Can you find the sum of all even numbers between 1 and 100?
4. What is the 20th term of the sequence \( 5 + 10 + 15 + \dots \)?
5. How can you derive the formula for the sum of an arithmetic series?

**Tip:** The formula for the sum of an arithmetic sequence can also be derived from the concept of the average of the first and last terms multiplied by the number of terms!

Learn how to calculate the sum of the arithmetic sequence 2 + 4 + 6 + ... + 70 using key concepts like arithmetic sequences and summation formulas. This step-by-step solution is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation