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Example 1

{18, 18, 14, 14, 10, 10, 6, 6, ...}

This sequence involves repetition and subtraction.

The numbers repeat themselves and then there is subtraction by four.

Example 2

Arithmetic sequences involve the addition or subtration of a constant to each term.

This sequence has a positive common difference of 7, (d=7).

{7, 14, 21, 28, 35, 42, 49, ...}

1. {60, 74, ?, 102, 116, ?, 144}

Answer: 88 and 130

Explanation: Add 14 to each preceding term.

2. {50, 68, ?, 122, 140, ?, 176}

Answer: 104 and 158

Explanation: Add 28 to each preceding term.

3. {99, 45, 54, 55, 18, 37, 44, 8, ?}

Answer: 44 - 8 = 36

Explanation: For every set of three numbers subtract the second number from the first.

4. {2, 1, 2, 5, 8, 16, 29, 43, ?}

Answer:16 + 29 + 43 = 88

Explanation: For every set of four numbers, add the previous three to arrive at the fourth.

5. {88, 82, 76, 70, 64, 58, ?}

Answer: 52

Explanation: Simple arithmetic series where six is subtracted from the previous term.