In number series questions, our goal is to identify the underlying pattern or rule that governs the sequence of numbers. Once the pattern is discovered, we can apply it to find the missing terms. Let's carefully analyze the given series to determine the relationship between consecutive numbers.

Series Analysis: Uncovering the Pattern

The given number series is:

\(10, 7, 6, 8, 5, 4, ?, ?\)

Let's examine the operations performed between successive terms in the series:

• From the first term (\(10\)) to the second term (\(7\)): \(10 - 3 = 7\). So, the operation is -3.
• From the second term (\(7\)) to the third term (\(6\)): \(7 - 1 = 6\). So, the operation is -1.
• From the third term (\(6\)) to the fourth term (\(8\)): \(6 + 2 = 8\). So, the operation is +2.
• From the fourth term (\(8\)) to the fifth term (\(5\)): \(8 - 3 = 5\). So, the operation is -3.
• From the fifth term (\(5\)) to the sixth term (\(4\)): \(5 - 1 = 4\). So, the operation is -1.

Let's list these operations sequentially:

\(-3, -1, +2, -3, -1\)

Upon observing these operations, we can identify a clear repeating pattern. The sequence of operations \(\left(-3, -1, +2\right)\) seems to repeat.

Identifying the Repeating Operations

The pattern of operations identified is a cycle of three steps: subtract 3, then subtract 1, then add 2. This cycle then repeats.

As shown in the table, the operations \(-3, -1, +2\) complete one cycle, and then the next cycle begins with \(-3, -1\). The series reaches \(4\) after the \(-1\) operation of the second cycle.

Calculating the Missing Terms

To find the next two missing terms, we need to continue the established pattern:

1. The last operation applied was \(-1\), which resulted in the term \(4\). According to the repeating pattern \(\left(-3, -1, +2\right)\), the next operation after \(-1\) should be \(+2\).
2. First Missing Term: Apply \(+2\) to the last known term, which is \(4\).

   \(4 + 2 = 6\)

   So, the first missing term is \(6\).

3. After the \(+2\) operation, the pattern cycle \(\left(-3, -1, +2\right)\) restarts. So, the next operation in the sequence will be \(-3\).
4. Second Missing Term: Apply \(-3\) to the newly found term, which is \(6\).

   \(6 - 3 = 3\)

   So, the second missing term is \(3\).

Therefore, the two missing terms in the series are \(6\) and \(3\) respectively.

The complete series becomes:

\(10, 7, 6, 8, 5, 4, 6, 3\)

This detailed analysis confirms that the pattern is consistent throughout the series, allowing us to accurately predict the missing values.