Find the sum of all even integers from 10 to 70 with solution

To find the sum of all even integers from 10 to 70, we can 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 last term.

### Step 1: Identify the first term, last term, and number of terms
- The first even integer in the range is \( a_1 = 10 \).
- The last even integer in the range is \( a_n = 70 \).
- The difference between consecutive terms (common difference) is \( d = 2 \).

### Step 2: Find the number of terms \( n \)
To find \( n \), use the formula for the \( n \)-th term of an arithmetic sequence:

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

Substitute the values:

\[
70 = 10 + (n-1) \times 2
\]

Solving for \( n \):

\[
70 = 10 + 2n - 2
\]
\[
70 = 8 + 2n
\]
\[
62 = 2n
\]
\[
n = \frac{62}{2} = 31
\]

There are 

Learn how to find the sum of all even integers from 10 to 70 using the arithmetic series sum formula. This problem involves identifying terms of an arithmetic sequence and calculating the sum. Suitable for students in Grades 6-8.

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