Find the next number in the given series: 9, 7, 10, 6, 11, ?

Introduction / Context:
This is a compact number series that uses alternating addition and subtraction with steadily increasing magnitudes. The goal is to identify this alternating pattern and then use it to predict the next term. Questions of this kind help develop your ability to track signs and magnitudes of changes in a sequence rather than just looking at raw values.

Given Data / Assumptions:

• Series: 9, 7, 10, 6, 11, ?
• Exactly one term is missing at the end.
• The changes between consecutive terms appear to alternate between increases and decreases.

Concept / Approach:
We focus on the differences between consecutive terms and look for two patterns at once: the sign of the change (positive or negative) and the size of the change. Many exam series alternate between adding and subtracting numbers whose magnitudes grow in a regular way such as 2, 3, 4, 5, and so on. Once the pattern is identified, extending the sequence is straightforward.

Step-by-Step Solution:
Step 1: Compute the differences between consecutive terms. 7 - 9 = -2. 10 - 7 = +3. 6 - 10 = -4. 11 - 6 = +5. Step 2: Observe that the signs alternate: minus, plus, minus, plus. Step 3: Observe the magnitudes: 2, 3, 4, 5. Each step increases by 1. Step 4: Following this pattern, the next difference should be negative again (to continue the alternation) and its magnitude should be 6 (the next integer after 5). Step 5: So the next difference is -6. Step 6: Apply this to the last known term: 11 + (-6) = 5.

Verification / Alternative check:
Now write the extended sequence: 9, 7, 10, 6, 11, 5. Recompute all differences: -2, +3, -4, +5, -6. The signs alternate perfectly and the absolute values form a simple increasing sequence 2, 3, 4, 5, 6. This double pattern provides a strong confirmation that 5 is the correct next term.

Why Other Options Are Wrong:
If we choose 4, 13, or 15, the final difference becomes -7, +2, or +4 respectively, none of which fit the combined rule of alternating signs with stepwise increasing magnitudes. For example, choosing 13 would give a last difference of +2, which breaks both the expected negative sign and the required magnitude of 6. Therefore these options do not match the clearly observed structure of the series.

Common Pitfalls:
Some candidates look only at values that go up and down and guess randomly, missing the exact numeric pattern of the differences. Others may identify the alternating signs but fail to notice that the sizes of the jumps increase steadily. Always examine both the sign and the magnitude of changes in alternating series problems.

Final Answer:
The next number that correctly completes the series is 5.