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Find the missing number in the series: 5, 7, 10, 15, 22, ?
30
31
33
35
33
Calculate the differences between consecutive terms to find the underlying sequence of prime numbers.
Calculate the differences between consecutive terms to find the underlying sequence of prime numbers.
Analyze the difference between terms
Calculate the difference between consecutive numbers: 7-5=2, 10-7=3, 15-10=5, 22-15=7.
Identify the pattern
The differences are 2, 3, 5, 7, which represent the sequence of consecutive prime numbers.
Calculate the missing number
The next prime number after 7 is 11. Adding this to the last term: 22 + 11 = 33.
A: 30 is incorrect as it implies a sequence of differences 2, 3, 5, 7, 8 which is not prime. B: 31 is incorrect as it would require the difference to be 9, which is a composite number. D: 35 is incorrect as it would require the difference to be 13, skipping the prime 11.
C is correct because the series follows a pattern of adding consecutive prime numbers (2, 3, 5, 7, 11) to each preceding term.
When a series increases slowly, always find the difference of differences; if the differences are prime, odd, or squared numbers, you have identified the logic.
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