Determine the next term: 10, 18, 28, 40, 54, 70, ? — identify the steadily growing even-number differences and extend the pattern.
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A85
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B86
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C87
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D88
Answer
Correct Answer: 88
Explanation
Introduction / Context:Many series grow by adding consecutively larger even numbers. Detecting that arithmetic progression within the differences yields the next term effortlessly.
Given Data / Assumptions:
- Series: 10, 18, 28, 40, 54, 70, ?
- We will analyze the first differences.
Concept / Approach:Compute step-by-step increases and look for a simple pattern, such as an arithmetic progression in the differences. Then apply the next difference to the last term.
Step-by-Step Solution:
Differences: 18 − 10 = 8; 28 − 18 = 10; 40 − 28 = 12; 54 − 40 = 14; 70 − 54 = 16.The differences are even numbers increasing by 2 each time: 8, 10, 12, 14, 16.Next difference = 18.Next term = 70 + 18 = 88.Verification / Alternative check:Extending the even-number progression maintains consistency; any other next term would break the +2 step in the differences.
Why Other Options Are Wrong:
- 85, 86, 87 correspond to differences 15, 16, 17 from 70, which break the clear +2 even-number pattern.
Common Pitfalls:Mistaking the pattern for multiplication or squares. The plain even-increment rule is both sufficient and consistent here.
Final Answer:88