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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.
22, 32, 42, 52.
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