Find the missing number in the following series. $24, 20, 29, ?, 38, 2$

This series follows an alternating pattern. Odd positions: 24, 29, 38 (differences: +5, +9). Even positions: 20, ?, 42. The pattern in differences increases by 4 each time (5→9→13→17→...). Continuing: 24→29 is +5, 29→38 is +9. For evens: 20→? should be -(5+4=9), so 20-9=11. But 38-13=25, and 25+17=42 works. However, answer given is 13. Another interpretation: 24→20 is -4, 20→29 is +9, 29→13 is -16, 13→38 is +25, 38→2 is -36. The differences (4,9,16,25,36) are squares of 2,3,4,5,6 with alternating signs. This makes the missing number 13 (29-16=13).