Determine the Pattern: What is the Rule for the Sequence 60, 50, 40, 30?

What is the term-to-term rule of the following sequence?

60, 50, 40, 30, ...

To solve this problem, we'll follow these steps:

• Step 1: Identify the common difference between the terms.
• Step 2: Use the formula for an arithmetic sequence to find the general formula for the nth term.

Now, let's work through each step:
Step 1: Observe the difference between consecutive terms: - The difference between the first and second terms (60 - 50) is 10. - The difference between the second and third terms (50 - 40) is also 10. - Similarly, the difference remains constant at 10 for the remaining terms (40 - 30 = 10).
Thus, the common difference $d$ is -10, as the terms are decreasing by 10 each time.

Step 2: Use the formula for an arithmetic sequence:
The nth term of an arithmetic sequence $a_n$ can be expressed as $a_n = a_1 + (n-1)d$, where $a_1$ is the initial term and $d$ is the common difference.
Here, $a_1 = 60$ and $d = -10$. Plugging these into the formula, we have:
$a_n = 60 + (n-1)(-10)$
Simplifying the expression:
$a_n = 60 - 10n + 10$
$a_n = 70 - 10n$
Thus, the nth term is $a_n = -10n + 70$.

Therefore, the term-to-term rule for this sequence is $-10n + 70$, which matches the correct answer choice $\boxed{-10n + 70}$.