In the arithmetic sequence of -7,-4,-1,2 which term is 44?​​​​

To find which term in the arithmetic sequence is equal to 44, we can use the general formula for the \(n\)-th term of an arithmetic sequence:

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

Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the position of the term.

### Step 1: Identify the first term \(a_1\) and the common difference \(d\)
- \(a_1 = -7\)
- The common difference \(d\) is found by subtracting the first term from the second term:
  \[
  d = -4 - (-7) = 3
  \]

### Step 2: Set up the equation to find \(n\)
We are looking for the term that equals 44, so set \(a_n = 44\):
\[
44 = -7 + (n - 1) \cdot 3
\]

### Step 3: Solve for \(n\)
1. Start by isolating the term involving \(n\):
   \[
   44 + 7 = (n - 1) \cdot 3
   \]
   \[
   51 = (n - 1) \cdot 3
   \]

2. Divide both sides by 3:
   \[
   \frac{51}{3} = n - 1
   \]
   \[
   17 = n - 1
   \]

3. Finally, solve for \(n\):
   \[
   n = 17 + 1 = 18
   \]

The term that equals 44 is the **18th term** in the arithmetic sequence.

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How do you find the sum of the first 18 terms of this arithmetic sequence?
2. What is the 25th term of this arithmetic sequence?
3. How can you determine if a sequence is arithmetic or not?
4. What happens to the general term formula if the common difference is negative?
5. How do you find the common difference if only two non-consecutive terms are given?

**Tip:** When solving for \(n\) in an arithmetic sequence, make sure to carefully isolate the variable by following each algebraic step methodically.

Discover how to find the 18th term in the arithmetic sequence -7, -4, -1, 2 using the nth term formula. This problem involves calculating the position of a specific term in an arithmetic sequence with a common difference of 3. Suitable for Grades 9-12.

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