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What should come in place of the question mark (?) in the given series? 68 76 86 98 112 ?
122
125
128
132
128
Observe the differences between consecutive terms: 8, 10, 12, 14... The difference is increasing by 2 in every step.
Observe the differences between consecutive terms: 8, 10, 12, 14... The difference is increasing by 2 in every step.
Analyze the differences
Calculate the difference between consecutive terms: 76-68=8, 86-76=10, 98-86=12, 112-98=14.
Identify the pattern
The differences are 8, 10, 12, 14. This is an arithmetic progression with a constant difference of 2. The next difference should be 14 + 2 = 16.
Calculate the missing term
Add the next difference to the last term: 112 + 16 = 128.
A: 122 is incorrect because it misses the pattern (112+10=122); B: 125 is mathematically inconsistent with the constant difference sequence; D: 132 is incorrect as it assumes a difference of 20 instead of 16.
C is correct because the series follows a pattern of adding consecutive even numbers starting from 8, resulting in 112 + 16 = 128.
In any number series, if the numbers grow slowly, always check the differences between consecutive terms first as it is the most common pattern.