Certainly! The sequence you provided is 18, 16, 14, 12. Let's solve it using the formula \( a_n = 2n \).

First, let's see if the given sequence fits the formula \( a_n = 2n \):

For \( n = 1 \):
\[ a_1 = 2(1) = 2 \]
However, the first term in your sequence is 18, not 2.

Let's analyze further if there might be a misunderstanding in the formula provided. It seems that the sequence you provided does not match the form \( a_n = 2n \) since all the terms are much higher than twice their position number.

Alternatively, if you meant to express the terms in the form of an arithmetic sequence using a different general form, let's re-evaluate. The given sequence appears to decrease by 2 each time. Hence, another approach to derive the sequence is as follows:

Given the formula \( a_n = a_1 + (n - 1)d \) and the first term \( a_1 = 18 \) and the common difference \( d = -2 \):

For \( n = 1 \):
\[ a_1 = 18 \]

For \( n = 2 \):
\[ a_2 = 18 + (2 - 1)(-2) = 18 - 2 = 16 \]

For \( n = 3 \):
\[ a_3 = 18 + (3 - 1)(-2) = 18 - 4 = 14 \]

For \( n = 4 \):
\[ a_4 = 18 + (4 - 1)(-2) = 18 - 6 = 12 \]

These calculations confirm that the given sequence is indeed an arithmetic sequence with a common difference of -2.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. What is the 10th term in this arithmetic sequence?
2. How would you find the sum of the first 20 terms of this sequence?
3. Can you write the formula for the nth term of this sequence?
4. How would the sequence change if the common difference was positive?
5. What is the general formula for the sum of the first n terms of an arithmetic sequence?
6. How does an arithmetic sequence differ from a geometric sequence?
7. Can you derive the nth term of this sequence using the given first term and common difference?
8. How would you graph this sequence on a coordinate plane?

**Tip:** When identifying the formula for a sequence, always verify that the proposed formula fits all given terms in the sequence.

Explore how to understand and solve arithmetic sequences with a decreasing pattern. This problem covers identifying the sequence's pattern, applying the arithmetic sequence formula, and calculating specific terms. Suitable for high school students studying arithmetic sequences.

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