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What should come in place of the two question marks (?) in the given series in the same order? 42, 43, 47, 56, ? , 97 , ?
72, 133
71, 132
74, 135
70, 131
72, 133
Observe the differences between consecutive terms: they follow the sequence of perfect squares starting from 1 squared (1, 4, 9, 16, 25, 36).
Observe the differences between consecutive terms: they follow the sequence of perfect squares starting from 1 squared (1, 4, 9, 16, 25, 36).
Analyze the differences between terms
Find the difference between consecutive numbers: 43 - 42 = 1, 47 - 43 = 4, 56 - 47 = 9. These are 1 squared, 2 squared, and 3 squared.
Predict the next differences
Following the pattern of squares (1┬▓, 2┬▓, 3┬▓, 4┬▓, 5┬▓, 6┬▓), the next differences should be 16 and 25, then 36.
Calculate missing terms
First missing term: 56 + 16 = 72. Verification: 72 + 25 = 97 (matches the given series). Final missing term: 97 + 36 = 133.
B: 71 and 132 do not follow the square difference pattern (56+15=71, 97+35=132). C: 74 and 135 do not follow the square difference pattern (56+18=74, 97+38=135). D: 70 and 131 do not follow the square difference pattern (56+14=70, 97+34=131).
A is correct because the series follows an addition pattern of consecutive perfect squares (1, 4, 9, 16, 25, 36), resulting in 56+16=72 and 97+36=133.
In number series, if the numbers grow slowly, always check the difference between terms first. If differences are not obvious, check if they are squares or cubes.
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