The next number in the sequence is 18.
It's +1, +2, +3, +4, ....
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Every next number is increased by 5. The next number in the sequence is 23.
42 is the next number in this sequence. This number sequence is adding the next prime number to the last number. So 1 + 2 = 3. Then 3 + 3 = 6, 6 + 5 = 11, 11 + 7 = 18, 18 + 11 = 29. The next prime number after 11 is 13, so 29 + 13 = 42. The next numbers would be 59 (42+17), 78 (59+19), and 101 (78+23)
23
22
The sequence is taking half of the number and adding it to that number, 3/2 = 1.5, 3 + 1.5 = 4.5, the next number in the sequence is 15.1875