What will come in place of the question mark (?) in the following number series, where the increments alternate between two values? 18, 29, 42, 53, ?, 77

Introduction / Context:
This series increases by two alternating differences. The learner must identify that the increments switch repetitively between two specific values. Recognising alternating addition patterns is a vital skill in many number series questions.

Given Data / Assumptions:
- Series: 18, 29, 42, 53, ?, 77. - The fifth term is missing. - The differences between terms appear to repeat in a pattern.

Concept / Approach:
Compute the differences between consecutive terms and look for repetition. If two values alternate, then this alternation can be extended to determine the missing increment and therefore the missing term. Checking both the earlier and later parts of the series ensures that the pattern is correct.

Step-by-Step Solution:
Step 1: Compute differences. 29 - 18 = 11. 42 - 29 = 13. 53 - 42 = 11. Step 2: The differences observed so far are 11, 13, and 11. Step 3: This suggests an alternating pattern: +11, +13, +11, +13, and so on. Step 4: The next difference after 11 should therefore be 13. Step 5: Add 13 to 53 to find the missing term: 53 + 13 = 66. Step 6: Confirm with the final step: 77 - 66 = 11, which fits the alternation of 11 and 13.

Verification / Alternative check:
Write out the pattern of differences explicitly: 18 + 11 = 29, 29 + 13 = 42, 42 + 11 = 53, 53 + 13 = 66, 66 + 11 = 77. This reconstruction confirms the alternating sequence of +11 and +13 and shows that 66 is the only value that keeps the pattern intact.

Why Other Options Are Wrong:
- Option 64 would give a difference of 11 from 53 but then require 13 to reach 77, which would not match the established order. - Option 71 would yield a difference of 18 from 53 and then 6 to reach 77, which does not fit the consistent pattern. - Option 65 introduces a difference of 12 that is not part of the alternating 11 and 13 structure.

Common Pitfalls:
Learners may miscalculate one of the differences and then fail to see the alternating pattern. Others might focus only on the first few terms and not confirm the pattern with later terms. A full check across the entire series is essential to avoid incorrect conclusions.

Final Answer:
The missing term in the series is 66, so the correct option is 66.