To solve the given problem, let's go through each step methodically:
1. Identify the Sequence:
The given sequence is: 2, 4, 6, 8, 10
2. Calculate the Common Difference:
The common difference, denoted as [tex]\(d\)[/tex], in an arithmetic sequence is found by subtracting the first term from the second term.
[tex]\[
d = 4 - 2 = 2
\][/tex]
3. Determine the Next Three Terms:
To find the next three terms in the sequence, we continue adding the common difference ([tex]\(d = 2\)[/tex]) to the last term in the sequence.
- First additional term:
[tex]\[
10 + 2 = 12
\][/tex]
- Second additional term:
[tex]\[
12 + 2 = 14
\][/tex]
- Third additional term:
[tex]\[
14 + 2 = 16
\][/tex]
4. Summarize the Results:
- The common difference ([tex]\(d\)[/tex]) is: 2
- The next three terms after 10 are: 12, 14, and 16
Let's put these findings together:
- Common Difference: 2
- Next Three Terms in the Sequence: 12, 14, 16
