Introduction / Context:
Here we have a decreasing series. Many such sequences reduce by amounts that grow steadily (e.g., −20, −25, −30, −35…). If one reduction breaks the step-size pattern, the corresponding term is the odd one out.
Given Data / Assumptions:
- Series: 105, 85, 60, 30, 0, −45, −90
- One term does not fit the intended decrement pattern.
Concept / Approach:
Compute consecutive differences and verify whether the decrements increase by 5 each time (a common construction). Identify any mismatch.
Step-by-Step Solution:
85 − 105 = −2060 − 85 = −2530 − 60 = −300 − 30 = −30 (should be −35 here)−45 − 0 = −45 (this would match the next step if previous were correct)−90 − (−45) = −45 (should then be −50 if strictly continuing)The fourth step should be −35, making 30 − 35 = −5, not 0. Thus 0 is the inconsistent term.
Verification / Alternative check:
Corrected sequence with −20, −25, −30, −35, −40, −45 steps: 105, 85, 60, 30, −5, −45, −90.
Why Other Options Are Wrong:
85, 60 align with −20 and −25; −45 and −90 can align with larger negative steps; they are plausible under the corrected pattern.
Common Pitfalls:
Accepting repeated −30 steps without checking the expected growth in decrement size.
Final Answer:
0
Discussion & Comments