Write an explicit formula for a$$ n,\text{ the }n $$th term of the sequence 32, 28, 24 ....


The given sequence is: 
\[
32, 28, 24, \dots
\]
This sequence is an arithmetic sequence because the difference between consecutive terms is constant. The common difference $ d $ is:
\[
d = 28 - 32 = -4
\]
The first term $ a_1 $ is 32.

The explicit formula for the $ n $-th term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Substituting the values of $ a_1 = 32 $ and $ d = -4 $, we get:
\[
a_n = 32 + (n - 1) \cdot (-4)
\]
Simplifying:
\[
a_n = 32 - 4(n - 1)
\]
\[
a_n = 32 - 4n + 4
\]
\[
a_n = 36 - 4n
\]

Thus, the explicit formula for the $ n $-th term of the sequence is:
\[
a_n = 36 - 4n
\]

Would you like more details on how arithmetic sequences work or have any other questions?

Here are 5 related questions you might find useful:
1. How do you find the sum of an arithmetic sequence?
2. What is the formula for the sum of the first $ n $ terms of an arithmetic sequence?
3. How can you determine if a sequence is arithmetic?
4. Can arithmetic sequences have positive and negative common differences?
5. How does the formula for geometric sequences differ from arithmetic ones?

**Tip:** In arithmetic sequences, the common difference between terms is always constant!

Write an explicit formula for the n-th term of the sequence 32, 28, 24 ....

Learn how to find the explicit formula for the arithmetic sequence 32, 28, 24 with step-by-step instructions. This solution covers key algebraic concepts, including arithmetic sequences, and is suitable for students in Grades 7-9.

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