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The sequence given is:

\[ 1, 6, 4, 11, 9, 16, 16, 21, \ldots \]

Let's analyze the pattern:

1. The differences between consecutive terms:
   - \( 6 - 1 = 5 \)
   - \( 4 - 6 = -2 \)
   - \( 11 - 4 = 7 \)
   - \( 9 - 11 = -2 \)
   - \( 16 - 9 = 7 \)
   - \( 16 - 16 = 0 \)
   - \( 21 - 16 = 5 \)

It seems that there are alternating differences:
- The differences are following a periodic pattern: \( +5, -2, +7, -2, +7, 0, +5 \).

To predict the next term:
- The pattern suggests that after a difference of \( +5 \), the next difference should be \( -2 \).
- Adding \( -2 \) to the last term \( 21 \): \( 21 + (-2) = 19 \).

Thus, the next term in the sequence should be \( 19 \).

However, this option isn't provided. Therefore, based on the provided options, the most reasonable assumption is that the answer lies within a different interpretational frame or the differences may have fluctuated slightly in the pattern. Since none of the answers directly match, a small error or variation in the next sequence value could occur at times.

Do you want further clarification? Below are 5 additional related questions:

1. What is the difference between an arithmetic and a geometric sequence?
2. How can you identify whether a sequence follows a regular pattern or is non-linear?
3. How do periodic sequences differ from arithmetic sequences?
4. What strategies can you use to identify complex sequences with alternating patterns?
5. Can you apply the same methods to sequences that grow exponentially instead of linearly?

**Tip:** Always try calculating multiple term differences when analyzing sequences; patterns may alternate or shift over different groups of terms.

1, 6, 4, 11, 9, 16, 16, 21, ... What is the next term in the sequence?

Explore how to determine the next term in the sequence 1, 6, 4, 11, 9, 16, 16, 21, using arithmetic patterns. This solution covers key mathematical concepts of differences between consecutive terms. Suitable for students in Grades 6-8.

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