Find the missing term: 8, 43, 11, 41, __, 39, 17, … Identify the value that fits the alternating-step pattern.

Introduction / Context:This sequence alternates between adding and subtracting shrinking amounts. The absolute size of the step decreases in a regular fashion across the series.

Given Data / Assumptions:

• Known terms: 8, 43, 11, 41, ?, 39, 17
• Exactly one term is missing between 41 and 39.

Concept / Approach:Compute consecutive differences and look at absolute values: 8→43 = +35; 43→11 = −32; 11→41 = +30. The magnitudes 35, 32, 30 suggest a pattern decreasing by 3, then 2, repeating over positive and negative steps.

Step-by-Step Solution:Following +35, −32, +30, the next should be a negative step with magnitude 27 (30 − 3).41 − 27 = 14, so the missing term is 14.Next difference should be +25 (27 − 2), and 14 + 25 = 39, which matches the next given term.

Verification / Alternative check:Continuing the rule would give the next step −22 (25 − 3): 39 − 22 = 17, which also matches the following term.

Why Other Options Are Wrong:

• 8 / 43 / 44: None satisfy both the required −27 step from 41 and the subsequent +25 to reach 39.

Common Pitfalls:Checking only one side of the blank. Always ensure the candidate fits both the prior and the subsequent term under a single consistent rule.

Final Answer:14