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IV. Directions: Determine the next two terms in the sequence, then write the rule for finding the nth terms. 1. 2, 5, 8, 11, _,Rule:2. 5, 3, 1, -1, , _Rule: _3. 1, 4, 9, 16, _,Rule:4. 4, 10, 28, 82, _, _Rule:5. 1, 6, 11, 16, _, _Rule: _​.

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Answer:

  1. [tex]2, 5, 8, 11, 14[/tex]
  2. [tex]5, 3, 1, -1, -3[/tex]
  3. [tex]1, 4, 9, 16, 25[/tex]
  4. [tex]4, 10, 28, 82, 244, 730[/tex]
  5. [tex]1, 6, 11, 16, 21, 26[/tex]

Explanation:

  1. Add [tex]3[/tex] to each number.
  2. Subtract [tex]2[/tex] to each number.
  3. Use the perfect square rule: [tex]4^2 = 16, 5^2 = 25[/tex]
  4. Each number in the series is [tex]2[/tex] less than thrice the preceding number.
  5. Add [tex]5[/tex] to each number.

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