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The terms in patterned sequences follow repeating patterns which may be increasing, decreasing or alternating accordingly.

Example 1

{2, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 2, 5, 5, 5, 2, ?, 5}

Answer:5.

Explanation: There is a decreasing order of 'fives' between the 'twos'.

Example 2

{1, 33, 666, ?, 1212121212, 151515151515, ?, 2121212121212121}

{10101010101010101010, 88888888, 666666 ?, 22}

Answer: 4444

Explanation: There are ten 10s, eight 8s, six 6s, four 4s, and two 2s

1. {1, 2, 4, 7, 8, 10, 13, ?}

Answer: 13 + 1 = 14

Explanation: The numbers one, two and three are being added in recurring order.

2. {9, 119, ?, 1513119, 171513119, 19171513119, 2119171513119}

Answer:13119, 232119171513119

Explanation: Insert consecutive odd numbers to the left of the proceeding term.

3. {2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, ?}

Answer: 54 x 3 = 162

Explanation: Triple each term for every consecutive set of three terms.

4. {4, 2, 4, 2, 4, 2, 4, 2, 4, 2, ?}

Answer: 4

Explanation: Digits are constantly alternating from four to two.

5. {3, 34, 345, 3456, 34567, 345678, ?}

Answer: 3456789

Explanation: Each term gains a digit incrementally bigger than the last digit of the preceeding term.