#### 16, 33, 65, 131, 261, (....)

Explanation: Each number is twice the preceding one with 1 added or subtracted alternatively. So, the next number is (2 x 261 + 1) = 523.

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#### 10, 5, 13, 10, 16, 20, 19, (....)

Explanation: There are two series (10, 13, 16, 19) and (5, 10, 20, 40), one increasing by 3 and the other multiplied by 2.

#### 2, 4, 12, 48, 240, (....)

Explanation: Go on multiplying the given numbers by 2, 3, 4, 5, 6. So, the correct next number is 1440.

#### 8, 7, 11, 12, 14, 17, 17, 22, (....)

Explanation: There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively.

#### 11, 13, 17, 19, 23, 29, 31, 37, 41, (....)

Explanation: Numbers are all primes. The next prime is 43.

#### 8, 24, 12, 36, 18, 54, (....)

Explanation: Numbers are alternatively multiplied by 3 and divided by 2. So, the next number = 54 รท 2 = 27.

#### 2, 6, 12, 20, 30, 42, 56, (....)

Explanation: The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8. So, the next number is 8 x 9 = 72.

#### 4, -8, 16, -32, 64, (....)

Explanation: Each number is the proceeding number multiplied by -2. So, the required number is -128.

#### 5, 10, 13, 26, 29, 58, 61, (....)

Explanation: Numbers are alternatively multiplied by 2 and increased by 3. So, the missing number = 61 x 2 = 122.

#### 15, 31, 63, 127, 255, (....)

Explanation: Each number is double the preceding one plus 1. So, the next number is (255 x 2) + 1 = 511.