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What should come in place of the question mark (?) in the given series?
82 85 95 112 136 ?
153
167
174
160
167
Quick Trick: Calculate the differences between consecutive terms: +3, +10, +17, +24. Notice they increase by +7 each step! The next difference is 24 + 7 = 31, so 136 + 31 = 167.
Calculate the differences between consecutive terms: +3, +10, +17, +24. Notice they increase by +7 each step! The next difference is 24 + 7 = 31, so 136 + 31 = 167.
Find the First Difference
Calculate the difference between consecutive terms in the given series: 85 - 82 = 3 95 - 85 = 10 112 - 95 = 17 136 - 112 = 24 So, the first-level differences are: 3, 10, 17, 24.
Find the Second Difference Pattern
Check the difference between consecutive first-level differences: 10 - 3 = 7 17 - 10 = 7 24 - 17 = 7 There is a constant common difference of +7.
Calculate the Missing Term
The next difference after 24 will be 24 + 7 = 31. Therefore, the missing term in the series is 136 + 31 = 167.
A: 153 is incorrect because it adds 17 instead of 31 to 136. C: 174 is incorrect because it adds 38 instead of 31 to 136. D: 160 is incorrect because it adds 24 instead of 31 to 136.
B is correct because the series follows a double difference pattern where the difference between consecutive terms increases by +7 each step, giving 136 + 31 = 167.
When first-level differences (+3, +10, +17, +24) do not form a standard pattern immediately, always calculate the second-level differences to check for a constant or changing difference rule.