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What should come in place of the question mark (?) in the given series? 78 79 83 92 108 ?
134
135
133
132
133
Calculate the differences between consecutive terms: the differences themselves form a sequence of squares (1 squared, 2 squared, 3 squared, 4 squared, 5 squared).
Calculate the differences between consecutive terms: the differences themselves form a sequence of squares (1 squared, 2 squared, 3 squared, 4 squared, 5 squared).
Analyze consecutive differences
Find the difference between each term: 79-78=1, 83-79=4, 92-83=9, 108-92=16.
Identify the pattern
The differences are 1, 4, 9, 16, which are squares of consecutive integers: 1 squared, 2 squared, 3 squared, and 4 squared.
Calculate the next term
The next difference must be 5 squared, which is 25. Adding 25 to the last term 108 gives 108 + 25 = 133.
A: 134 is incorrect as it implies a +26 difference. B: 135 is incorrect as it implies a +27 difference. D: 132 is incorrect as it implies a +24 difference.
C is correct because the series follows a pattern of adding increasing squares (1, 4, 9, 16, 25) to the preceding number.
In number series, if the numbers grow slowly, always check the difference between terms first. If the difference is not constant, check the squares or cubes of numbers.
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