Find the 12th term of the arithmetic sequence 5x−6,9x−10,13x−14,

To find the 12th term of the given arithmetic sequence, we first need to determine the common difference and then use the formula for the \(n\)th term of an arithmetic sequence.

### Step 1: Identify the first term (\(a_1\)) and the common difference (\(d\))
The given sequence is:
\[
5x - 6, \quad 9x - 10, \quad 13x - 14, \ldots
\]
- The first term \(a_1 = 5x - 6\).
- The second term \(a_2 = 9x - 10\).

The common difference \(d\) is calculated as:
\[
d = a_2 - a_1 = (9x - 10) - (5x - 6)
\]
\[
d = 9x - 10 - 5x + 6 = 4x - 4
\]

### Step 2: Use the formula for the \(n\)th term of an arithmetic sequence
The formula for the \(n\)th term (\(a_n\)) of an arithmetic sequence is:
\[
a_n = a_1 + (n-1) \cdot d
\]

### Step 3: Substitute the values for \(n = 12\), \(a_1\), and \(d\)
\[
a_{12} = (5x - 6) + (12 - 1) \cdot (4x - 4)
\]
\[
a_{12} = (5x - 6) + 11 \cdot (4x - 4)
\]
\[
a_{12} = (5x - 6) + (44x - 44)
\]
\[
a_{12} = 5x - 6 + 44x - 44
\]
\[
a_{12} = 49x - 50
\]

So, the 12th term of the arithmetic sequence is \( \boxed{49x - 50} \).

Would you like to go over the details, or do you have any further questions? Here are some related questions you might find interesting:

1. How do you find the sum of the first 12 terms of this arithmetic sequence?
2. What is the 20th term of this sequence?
3. How do you determine whether a sequence is arithmetic?
4. Can you find the common difference of an arithmetic sequence from any two terms?
5. How would you solve for \(x\) if the 12th term is given?

**Tip:** In arithmetic sequences, knowing just two terms is enough to find the common difference and thus determine any term in the sequence.

Find the 12th term of the arithmetic sequence 5x−6, 9x−10, 13x−14.

Find the 12th term of the arithmetic sequence 5x−6, 9x−10, 13x−14 with a step-by-step solution. Learn how to identify the first term, calculate the common difference, and apply the nth term formula. Suitable for students in Grades 8-10.

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