How to get the general formula for this stem 2 4 6

To find the general formula for the sequence \(2, 4, 6\) labeled "STEM," you can observe that it is an arithmetic sequence. An arithmetic sequence has the general form:

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

where:
- \(a_n\) is the \(n\)th term,
- \(a_1\) is the first term,
- \(d\) is the common difference between consecutive terms,
- \(n\) is the term number.

For the sequence \(2, 4, 6\):

1. **First term (\(a_1\))**: The first term \(a_1 = 2\).
2. **Common difference (\(d\))**: The common difference \(d = 4 - 2 = 2\).

Now, substitute these values into the general formula:

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

Simplifying the expression:

\[
a_n = 2 + 2n - 2
\]
\[
a_n = 2n
\]

So, the general formula for the \(n\)th term of the "STEM" sequence is:

\[
a_n = 2n
\]

This means the \(n\)th term is obtained by multiplying \(n\) by 2.

Would you like to explore further applications of this formula, or would you like help with other sequences? Here are five related questions:

1. How would you apply this formula to find the 10th term of the sequence?
2. How does this formula change if the first term is different?
3. What is the sum of the first \(n\) terms of this sequence?
4. Can this sequence be represented graphically, and what would its graph look like?
5. How would you derive a formula for a non-arithmetic sequence?

**Tip:** When working with sequences, always check the common difference first. If it's consistent, the sequence is arithmetic, and you can apply the general formula directly.

Discover the general formula for the arithmetic sequence 2, 4, 6. Understand how to derive the formula using the first term and the common difference. Suitable for Grades 7-9 mathematics curriculum.

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