We are given the arithmetic sequence with the first term $a_1 = 7$ and the second term $a_2 = 2$. We need to find the term number $n$ for which the value of the term is $-18$.

Step 1: Find the common difference $d$

The common difference $d$ is the difference between the second term and the first term: $d = a_2 - a_1 = 2 - 7 = -5$

Step 2: Use the formula for the $n$-th term

The general formula for the $n$-th term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \times d$ We are asked to find $n$ when $a_n = -18$, $a_1 = 7$, and $d = -5$. Substituting these values into the formula: $-18 = 7 + (n - 1) \times (-5)$

Step 3: Solve for $n$

First, subtract 7 from both sides: $-18 - 7 = (n - 1) \times (-5)$ $-25 = (n - 1) \times (-5)$

Now, divide both sides by -5: $n - 1 = \frac{-25}{-5} = 5$

Finally, add 1 to both sides: $n = 5 + 1 = 6$

Answer:

The term $-18$ is the 6th term of the arithmetic sequence.

Would you like further details or have any questions?

Here are some related questions to explore:

1. What is the 10th term of this sequence?
2. How would you find the sum of the first 20 terms of this sequence?
3. What if the common difference were positive? How would that affect the sequence?
4. How do you find the number of terms between two given terms in an arithmetic sequence?
5. How can you apply arithmetic sequences to financial calculations?

Tip: In arithmetic sequences, once you know the common difference and the first term, you can quickly calculate any term using the general formula!