To find the formula for the nth term of this arithmetic sequence:

The sequence provided is:

$a_1 = 28, \quad a_2 = 21, \quad a_3 = 14, \quad a_4 = 7$

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

The common difference is calculated by subtracting consecutive terms:

$d = a_2 - a_1 = 21 - 28 = -7$

Step 2: General formula for the nth term of an arithmetic sequence

The formula for the nth term is:

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

Step 3: Substitute values of $a_1 = 28$ and $d = -7$

$a_n = 28 + (n-1) \cdot (-7)$

Simplify:

$a_n = 28 - 7n + 7$

$a_n = -7n + 35$

Final Answer:

The formula for the nth term is:

$a_n = -7n + 35$

Would you like me to explain why the common difference affects the slope? Here are some related questions:

1. How do you determine if a sequence is arithmetic?
2. Why is the common difference important in an arithmetic sequence?
3. How can you find the sum of the first $n$ terms of an arithmetic sequence?
4. What happens when the common difference is positive instead of negative?
5. How can you use the nth term formula to solve real-world problems?

Tip: The common difference is always added repeatedly to the first term in an arithmetic sequence.