The following sequence is generated by dividing 50 by natural numbers :
0, 0, 2, 2, 0, 2, x, 2, 5, ...
What is x?

The sequence is generated by calculating the remainder when 50 is divided by consecutive natural numbers (n = 1, 2, 3, ...). By applying this rule, we can determine the terms of the sequence as follows:

• n = 1: 50 ÷ 1 = 50, remainder 0
• n = 2: 50 ÷ 2 = 25, remainder 0
• n = 3: 50 ÷ 3 = 16, remainder 2
• n = 4: 50 ÷ 4 = 12, remainder 2
• n = 5: 50 ÷ 5 = 10, remainder 0
• n = 6: 50 ÷ 6 = 8, remainder 2
• n = 7: 50 ÷ 7 = 7, remainder 1 (This is x)
• n = 8: 50 ÷ 8 = 6, remainder 2
• n = 9: 50 ÷ 9 = 5, remainder 5

The sequence formed is 0, 0, 2, 2, 0, 2, 1, 2, 5, ... matching the question's pattern. Thus, the value of x is 1.