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What should come in place of the question mark (?) in the given series? 901 903 ? 913 921 931
909
906
907
905
907
Observe the differences between consecutive terms; the series follows a pattern of adding consecutive prime numbers starting from 2.
Observe the differences between consecutive terms; the series follows a pattern of adding consecutive prime numbers starting from 2.
Analyze the differences between terms
Find the gap between each consecutive term: 903-901 = 2, 913-903 = 10, 921-913 = 8, 931-921 = 10.
Evaluate the pattern
Looking at the sequence 901, 903, ?, 913, 921, 931: The gaps are +2, ?, ?, +8, +10. The series represents adding consecutive prime numbers starting from 2: 901+2=903, 903+4=907 (Composite gap not prime?), actually re-evaluating: 901+2=903, 903+4=907, 907+6=913, 913+8=921, 921+10=931. The pattern is adding consecutive even numbers: +2, +4, +6, +8, +10.
Verify the result
If we add 4 to 903, we get 907. Adding 6 to 907 gives 913. Adding 8 to 913 gives 921. Adding 10 to 921 gives 931. The pattern +2, +4, +6, +8, +10 holds perfectly.
A: 909 results in a difference of 6 then 4, breaking the even number progression. B: 906 results in an odd difference (3), breaking the even number progression. D: 905 results in a difference of 2 then 8, breaking the sequence continuity.
C is correct because the series follows a consistent addition of consecutive even numbers starting from 2 (+2, +4, +6, +8, +10), making 903+4 = 907.
In number series questions, always calculate the difference between the first three terms first; if the differences are not constant, check for arithmetic progressions or square/cube related offsets.
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