A number series is given with one term missing. Examine the alternating pattern in 68, 72, 65, 69, 62, 66, ? and choose the correct alternative that completes the series.

Introduction / Context:
This number series question involves an alternating pattern of increases and decreases. The given sequence is 68, 72, 65, 69, 62, 66, ?, and we must find the missing last term. Such series commonly use two alternating operations, for example adding a fixed number and then subtracting another fixed number in a repeating cycle.

Given Data / Assumptions:
Series: 68, 72, 65, 69, 62, 66, ?
One term is missing at the end of the series.
The sequence appears to alternate between an increase and a decrease.
We assume a simple repeating pattern governs the entire series.

Concept / Approach:
We calculate consecutive differences and look for repetition. If we see, for example, +4, -7, +4, -7, and so on, we can extrapolate the pattern. This type of alternating addition and subtraction is a very common structure in verbal reasoning number series questions and should be checked early.

Step-by-Step Solution:
Compute the differences between consecutive terms. 72 - 68 = 4 (increase of 4). 65 - 72 = -7 (decrease of 7). 69 - 65 = 4 (increase of 4). 62 - 69 = -7 (decrease of 7). 66 - 62 = 4 (increase of 4). The pattern of differences is +4, -7, +4, -7, +4, ... Following this alternating pattern, the next difference should be -7. So, the missing term is 66 - 7 = 59. Therefore, the correct answer is 59.

Verification / Alternative check:
Reconstruct the extended sequence: 68, 72, 65, 69, 62, 66, 59. The differences are +4, -7, +4, -7, +4, -7, which shows a perfectly consistent alternating pattern. No other option creates such a clean alternation of +4 and -7, so 59 is the only valid choice.

Why Other Options Are Wrong:
Option A: 61 would give a difference of -5 from 66, which does not match the recurring -7 change.
Option C: 68 would mean a difference of +2, breaking the established +4 and -7 cycle.
Option D: 75 results in a difference of +9, which is inconsistent with earlier steps.
Option E: 63 gives a difference of -3, again violating the repeating pattern of -7 after each +4.

Common Pitfalls:
One common error is to look for a single arithmetic progression rather than noticing the alternation of adding and subtracting. Another pitfall is to miscalculate one of the differences and then search for an incorrect pattern based on that error. Carefully computing all differences and checking for a simple repeating cycle can greatly simplify many number series questions.

Final Answer:
The term that maintains the alternating pattern of +4 and -7 is 59, so the correct option is 59.