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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.