Complete the Decimal Sequence: Finding Missing Terms in 0.1 to 0 Pattern

To solve this mathematical sequence problem, we need to identify the common difference and use it to find the missing numbers. Let's follow these steps:

• Step 1: Identify the given numbers and their positions in the sequence.
• Step 2: Calculate the common difference between successive terms.
• Step 3: Use the common difference to determine the missing numbers.
• Step 4: Validate the completed sequence with the original pattern.

Now, let's work through each step:

Step 1: The given numbers in the sequence are $0.1, ?, 0.06, 0.04, ?, 0$.

Step 2: Calculate the common difference. The difference between $0.06$ and $0.04$ is $0.06 - 0.04 = 0.02$. The difference between $0.04$ and the next number $(0)$ is also $0.04 - 0 = 0.04$. This suggests a pattern of reducing by $0.02$ each time.

Step 3: Deduct $0.02$ from each preceding term to find the subsequent numbers:

• Before $0.06$, the number must be $0.06 + 0.02 = 0.08$.
• Before $0$, the number must be $0 + 0.02 = 0.02$.

Step 4: By substituting the above values into the sequence, we have the completed sequence: $0.1, 0.08, 0.06, 0.04, 0.02, 0$.

Therefore, the missing numbers in the sequence are $0.08$ and $0.02$.