Let's analyze the general patterns for each sequence:

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1.) 85, 79, 73, 67, 61,...

• This is an arithmetic sequence, where each term decreases by 6.
  • Difference: $85 - 79 = 6$, $79 - 73 = 6$, and so on.
  • General form: $a_n = 85 - 6(n-1)$

Pattern: Decreasing by 6.

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2.) 15, 22, 29, 36,...

• This is an arithmetic sequence, where each term increases by 7.
  • Difference: $22 - 15 = 7$, $29 - 22 = 7$, and so on.
  • General form: $a_n = 15 + 7(n-1)$

Pattern: Increasing by 7.

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3.) 4, 8, 12, 16, 20,...

• This is an arithmetic sequence, where each term increases by 4.
  • Difference: $8 - 4 = 4$, $12 - 8 = 4$, and so on.
  • General form: $a_n = 4 + 4(n-1)$

Pattern: Increasing by 4.

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4.) 1, 5, 11, 19, 29,...

• This is a quadratic sequence where the second differences are constant.
  • First differences: $5 - 1 = 4$, $11 - 5 = 6$, $19 - 11 = 8$, and so on.
  • Second differences: $6 - 4 = 2$, $8 - 6 = 2$, and so on.
  • General form (quadratic): $a_n = n^2 + n - 1$

Pattern: Quadratic pattern with second difference constant.

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5.) 8, 19, 34, 53,...

• This is another quadratic sequence, as the second differences are constant.
  • First differences: $19 - 8 = 11$, $34 - 19 = 15$, $53 - 34 = 19$.
  • Second differences: $15 - 11 = 4$, $19 - 15 = 4$.
  • General form (quadratic): $a_n = 2n^2 + 5n + 1$

Pattern: Quadratic pattern with constant second differences.

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Would you like any further details or clarifications on any of these sequences?

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Here are 5 related questions:

1. What is the next term in the first sequence?
2. Can you generalize the formula for the second sequence?
3. How do you determine if a sequence is quadratic or arithmetic?
4. What are the first 10 terms of the third sequence?
5. How would you derive the quadratic form of the fourth sequence?

Tip: When analyzing sequences, always check for constant differences between terms; this helps to identify whether the sequence is arithmetic, geometric, or quadratic.