Difficulty: Medium
Correct Answer: 98
Explanation:
Introduction / Context:
This question involves a number series where the differences between terms are not constant but show a regular progression. Recognising how these differences grow from term to term is the key to predicting the next number in the sequence.
Given Data / Assumptions:
Concept / Approach:
We first calculate the differences between consecutive terms. If these differences grow or shrink in a regular way, such as adding a constant amount, we can extrapolate that pattern to determine the next difference and hence the next term.
Step-by-Step Solution:
Step 1: Compute first differences: 14 - 8 = 6, 26 - 14 = 12, 44 - 26 = 18, 68 - 44 = 24.Step 2: The differences are 6, 12, 18 and 24.Step 3: Each difference increases by 6: 12 - 6 = 6, 18 - 12 = 6 and 24 - 18 = 6.Step 4: Therefore the next difference should be 24 + 6 = 30.Step 5: Add this to the last term in the series: 68 + 30 = 98.
Verification / Alternative check:
We can see the difference sequence explicitly as multiples of 6: 6 × 1, 6 × 2, 6 × 3 and 6 × 4. The next difference should naturally be 6 × 5 = 30. Using any other value for the difference would break this neat multiplication pattern. Thus 98 fits perfectly as the next term.
Why Other Options Are Wrong:
Values such as 94, 96, 102 or 112 correspond to differences of 26, 28, 34 and 44 from 68, none of which continues the multiples of 6 pattern. They therefore disrupt the observed second level structure and must be discarded.
Common Pitfalls:
Some learners may guess the next number based on approximate growth without explicitly computing differences, which can easily lead to wrong answers. Always computing the difference pattern is a reliable way to decode such series questions.
Final Answer:
The next term that maintains the pattern of increasing differences is 98.
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