what is the core of the pattern 10, 12, 14, 16

The given sequence is: 10, 12, 14, 16. 

This is an **arithmetic sequence** because the difference between consecutive terms is constant. The common difference (**d**) can be found by subtracting any two consecutive terms:

\[
d = 12 - 10 = 2
\]

Thus, the core of this pattern is that each term increases by 2.

To express the general term of the sequence (denoted as \( a_n \)), you can use the formula for an arithmetic sequence:

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

Where:
- \( a_1 = 10 \) (the first term),
- \( d = 2 \) (the common difference),
- \( n \) is the position of the term in the sequence.

So, the general term formula becomes:

\[
a_n = 10 + (n - 1) \cdot 2 = 10 + 2n - 2 = 2n + 8
\]

Thus, the core rule for generating the sequence is: **Start at 10 and add 2 for each subsequent term.**

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you find the 10th term of this sequence?
2. Can you determine the 50th term using the general formula?
3. What is the sum of the first 10 terms of this sequence?
4. What is the pattern if the sequence started at 20 instead of 10?
5. How do you determine if a sequence is arithmetic or geometric?

**Tip:** The sum of an arithmetic sequence can be quickly found using the formula \( S_n = \frac{n}{2} \cdot (a_1 + a_n) \).

Learn the core of the arithmetic pattern for the sequence 10, 12, 14, 16, where each term increases by 2. Explore key concepts of arithmetic sequences, including the general term formula and common difference. 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