To solve this problem, we need to identify the explicit formula for the arithmetic sequence given in the table. Here's the process:

Sequence Analysis

From the table:

• $a_1 = 9.2$ (first term)
• $a_2 = 7.4$
• $a_3 = 5.6$
• $a_4 = 3.8$
• $a_5 = 2$

Step 1: Find the common difference ($d$)

The difference between consecutive terms is: $d = a_{n+1} - a_n$ $d = 7.4 - 9.2 = -1.8$

Step 2: Explicit formula for an arithmetic sequence

The explicit formula for an arithmetic sequence is: $a_n = a_1 + (n-1)d$ Substitute $a_1 = 9.2$ and $d = -1.8$: $a_n = 9.2 + (n-1)(-1.8)$ Simplify: $a_n = 9.2 - 1.8(n-1)$

Step 3: Match with given options

The correct answer matches this formula. From the options:

• Correct answer: $a_n = 9.2 + (-1.8)(n-1)$

Let me know if you'd like further clarification!

Expansion Questions:

1. How do you calculate the common difference in any arithmetic sequence?
2. What happens to the formula if the common difference is positive?
3. How can you verify if a given sequence is arithmetic?
4. What adjustments are needed for finding the nth term if the sequence starts at $a_0$ instead of $a_1$?
5. How does the explicit formula change for geometric sequences?

Tip: Always double-check the sign of the common difference to