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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.