Number series with a functional step: 48, 23, ?, 4.25, 1.125 Find the missing third term by identifying the rule applied at each step.

Introduction / Context:Series sometimes evolve by repeatedly applying the same function rather than adding a constant difference. Here values drop sharply, hinting at a halving or fractional operation plus a small adjustment.

Given Data / Assumptions:

• Known terms: 48, 23, ?, 4.25, 1.125
• We search for a consistent term-to-term map f(x) that fits all given steps.

Concept / Approach:Test simple transformations such as x/2, x/2 ± 1, or (x ± c)/k. Check whether one rule fits both 48 → 23 and 4.25 → 1.125. If so, apply it to 23 to recover the missing middle term.

Step-by-Step Solution:Check 48 → 23 via x/2 − 1: 48/2 − 1 = 24 − 1 = 23 (fits).Check 4.25 → 1.125 via x/2 − 1: 4.25/2 − 1 = 2.125 − 1 = 1.125 (fits).Apply to 23 to get the missing term: 23/2 − 1 = 11.5 − 1 = 10.5.

Verification / Alternative check:Forward: 10.5/2 − 1 = 5.25 − 1 = 4.25, consistent with the displayed continuation.

Why Other Options Are Wrong:10, 2.5, and 11 do not satisfy the same function across all the checked steps; they would break the uniform mapping.

Common Pitfalls:Assuming pure halving (x/2) without the small offset; testing only one transition and not validating against others.

Final Answer:10.5