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What should come in place of тАШ?тАЩ in the given series? 12 18 27 39 54 ?
68
70
72
75
72
Calculate the differences between consecutive terms to find the secondary arithmetic progression pattern; the differences increase by 3 each step.
Calculate the differences between consecutive terms to find the secondary arithmetic progression pattern; the differences increase by 3 each step.
Calculate consecutive differences
Find the difference between each pair: 18-12=6, 27-18=9, 39-27=12, 54-39=15.
Identify the pattern of differences
The differences are 6, 9, 12, 15, which form an arithmetic progression increasing by 3 each time.
Determine the next term
Following the pattern, the next difference must be 15+3=18. Adding this to the last term: 54+18=72.
A: 68 is incorrect because the difference pattern requires adding 18 to 54, resulting in 72, not 68. B: 70 is incorrect because it does not follow the increment of 18 from 54. D: 75 is incorrect because adding 21 instead of 18 would violate the consistent +3 progression in differences.
C is correct because the series follows a pattern of adding consecutive multiples of 3 (6, 9, 12, 15, 18) to each preceding number.
When a series does not show a clear multiplication or square pattern, always write down the difference between terms to reveal potential hidden arithmetic or geometric sequences.
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