sequence: 21, 17, 13, 9, in what position does the term -3 appear?

The given sequence is: \(21, 17, 13, 9, \dots\).

This sequence is an arithmetic sequence because each term decreases by a constant difference. Let's find the common difference (\(d\)):

\[
d = 17 - 21 = -4
\]

The first term (\(a_1\)) is 21.

The general formula for the \(n\)-th term (\(a_n\)) of an arithmetic sequence is:

\[
a_n = a_1 + (n-1) \times d
\]

We need to find the position \(n\) at which the term \(-3\) appears. Set \(a_n = -3\):

\[
-3 = 21 + (n-1) \times (-4)
\]

Solve for \(n\):

\[
-3 = 21 - 4(n-1)
\]

\[
-3 = 21 - 4n + 4
\]

\[
-3 = 25 - 4n
\]

\[
4n = 25 + 3
\]

\[
4n = 28
\]

\[
n = \frac{28}{4} = 7
\]

So, the term \(-3\) appears in the **7th position** of the sequence.

Would you like further details or have any questions?

Here are five related questions you might consider:

1. How do you find the common difference in an arithmetic sequence?
2. What is the general formula for the \(n\)-th term of an arithmetic sequence?
3. How do you determine the sum of the first \(n\) terms of an arithmetic sequence?
4. How would the sequence change if the common difference was positive?
5. How can you identify whether a sequence is arithmetic or geometric?

**Tip:** Remember, in arithmetic sequences, the common difference can be positive or negative, affecting whether the sequence increases or decreases.

Learn how to find the position of the term -3 in an arithmetic sequence with a step-by-step solution. Understand the formula for the n-th term of an arithmetic sequence and how to apply it. Suitable for Grades 7-9.

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