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A number series may be composed of two or more separate alternating sequences
Example 1
{22, 320, 19, 160, 16, 80, 13, 40, 10, 20, 7,...}
The first series is an arithmetic progression with a common difference of minus three:
{22, 19, 16, 13, 10, 7, ...}
The second series is an geometric progression with a common ratio of a half:
{320, 160, 80, 40, 20, 10, ...}
Example 2
{108, 98, 88, 88, 78, ?, 68, 58, 88, 48, 38}
Answer: 88
Arithmetic progressions with a constant.
The first sequence starts 108 with a minus ten common difference.
The second sequence is the constant 88, every third term.
1. {0, 100, 20, ?, 40, 80, 60, 70, 80, ?, 100, 50}
Answer:90 and 60
Explanation: There are two alternating sequences.
The first one adds 20, and the second subtracts 10.
{0,20,40,60,80,100}
{100,90,80,70,60,50}
2. {2.5, 4, 4.5, 7, 8.5, 12, 18.5, 19, ?}
Answer: 22.5
Explanation: Two separate series.
Sequence A: {2.5, 4.5, 8.5, 16.5, ...}
The differences between the terms are: +2, +4, +8
Sequence B: {4, 7, 12, 19, ...}
The differences between the terms are: +3, +5, +7
3. {4, 4, 8, 8, 16, 12, 32, 16, 64, ?}
Answer: 4 x 5 = 20
Explanation: Two separate series.
Sequence A: {4, 4x2, 4x4, 4x8, 4x16}
The differences between the terms are: x2, x4, x8, x16
Sequence B: {4x1, 4x2, 4x3, 4x4, 4x5 = 20}
The differences between the terms are: x1, x2, x3, x4
4. {5, 10, 6, 11, 7, 12, 8, ?}
Answer: 13
Explanation: Two separate series.
{5, 6, 7, 8}
{10, 11, 12, 13}
5. {5, 1, 8, -1, 11, -3, 14, -5, 17, ?}
Answer: -7
Explanation: This is a twin series.
In the first sequence there a common difference of +3, while in the second sequence, the progression is -2.