Number series – fill in the missing term. Sequence: 72, 76, 73, 77, 74, __, 75, …

Introduction / Context:
This sequence alternates between two simple operations. Many exam series use a “+x, −y, +x, −y” motif. Spotting the cycle allows you to compute the missing term quickly and confidently.

Given Data / Assumptions:

• Given terms: 72, 76, 73, 77, 74, __, 75, …
• Clear alternation in direction: up, down, up, down, …
• Magnitudes of the up and down moves appear stable.

Concept / Approach:

Compute consecutive differences and look for a repeating 2-step pattern. Then apply that pattern to the position of the blank.

Step-by-Step Solution:

Verification / Alternative check:

Alternating increments of +4 and −3 reproduce every given step and predict the blank as 78. The following provided term 75 aligns via the −3 move, validating the solution.

Why Other Options Are Wrong:

70 or 71 would require −4 or −3 at the wrong point in the cycle. 75 repeats prematurely. Only 78 keeps the established +4/−3 alternation intact.

Common Pitfalls:

Assuming constant differences or overlooking simple two-step cycles. Always list differences and search for repeating patterns.

Final Answer:

78