find the 6th term of this 9, 4, -1, -6, -11

The given sequence is: 9, 4, -1, -6, -11. To find the 6th term, we need to determine the pattern of the sequence.

The difference between each pair of consecutive terms is:
- 4 - 9 = -5
- -1 - 4 = -5
- -6 - (-1) = -5
- -11 - (-6) = -5

The common difference \( d \) is -5, indicating this is an arithmetic sequence.

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

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

where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term, and
- \( d \) is the common difference.

Plugging in the known values:

- \( a_1 = 9 \)
- \( d = -5 \)
- \( n = 6 \)

\[ a_6 = 9 + (6 - 1)(-5) \]
\[ a_6 = 9 + 5(-5) \]
\[ a_6 = 9 - 25 \]
\[ a_6 = -16 \]

So, the 6th term is \(-16\).

Would you like further details or have any questions?

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Here are 8 related questions:
1. What is the 10th term of the sequence?
2. How do you find the sum of the first 10 terms in this sequence?
3. What is the general formula for the \( n \)-th term of an arithmetic sequence?
4. How do you identify whether a sequence is arithmetic or geometric?
5. Can a sequence have a common difference of zero? What would it look like?
6. How does the common difference affect the growth or decay of an arithmetic sequence?
7. What happens if the common difference is positive?
8. How do you calculate the number of terms in an arithmetic sequence given the first term, common difference, and last term?

**Tip:** In an arithmetic sequence, if the common difference is negative, the terms decrease; if positive, they increase.

Learn how to find the 6th term of the arithmetic sequence 9, 4, -1, -6, -11 using the arithmetic sequence nth term formula. Understand the pattern and calculation method involved. Suitable for students in Grades 7-9.

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