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Term differences are patterns that are apparent in the differences between the terms of a number sequence.

Example 1

{4, 8, 17, 33, 58, ...}

The differences between the terms are all squares.

2^{2}, 3^{2}, 4^{2}, 5^{2}.

Example 2

{1, 2, 7, 32, 157, 682...}

The differences between the terms have a common ratio of five.

1, 5, 25, 125, 625

1. {8, 12, 18, 26, 36, 48, ?}

Answer:(48 + 14) = 62

Explanation: The differences between the terms follow a plus two artithmetic progression.

4,6,8,10,12,14

2. {10, 20, 50, 140, ?}

Answer: 140 + 270 = 410

Explanation: The differences follow a geometric sequence with a common ratio of three.

10, 30, 90, 270.

3. {4, 10, 20, 34, 52, ?}

Answer: 52 + 22 = 74

Explanation: The common difference of the term differences is plus four.

6,10,14,18,22

4. {7,16,32,57,93,?}

Answer: 92 + 49 = 141

Explanation: The differences between the terms are all squares.

3^2, 4^2, 5^2, 6^2, 7^2

5. {1, 4, 10, 19, 31, ?}

Answer: 31 + 15 = 46

Explanation: The differences between the terms are multiples of three.

3, 6, 9, 12, 15