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3, 1, 7, 3, 13, 7, 21, 15, 31, 31, ?, 63, 57       
  • a)
    41                                       
  • b)
    39   
  • c)
    38                                       
  • d)
    43
Correct answer is option 'D'. Can you explain this answer?
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3, 1, 7, 3, 13, 7, 21, 15, 31, 31, ?, 63, 57a)41 b)39 c)38 d)43Correct...
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3, 1, 7, 3, 13, 7, 21, 15, 31, 31, ?, 63, 57a)41 b)39 c)38 d)43Correct...
3, 1, 7, 3, 13, 7, 21, 15, 31, 31, ?, 63, 57
Divide the given sequence into two parts taking alternate numbers

That is - 3,7,13,21,31,?,57. and 1,3,7,15,31,63

in first sequence it follows +4,+6,+8,10,+12,+14 (increasing by 2)
so the ? is 31+12 = 43

Second sequence follows
+2,+4,+8,+16,+32 (double of the previous)
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3, 1, 7, 3, 13, 7, 21, 15, 31, 31, ?, 63, 57a)41 b)39 c)38 d)43Correct...
The given sequence is: 3, 1, 7, 3, 13, 7, 21, 15, 31, 31, ?, 63, 57

To solve this sequence, we need to identify the pattern or rule that governs the numbers.

Observations:
- The pattern seems to alternate between two different sequences.
- The first sequence is 3, 7, 13, 21, 31, which is increasing by 4 each time.
- The second sequence is 1, 3, 7, 15, 31, which is increasing by doubling the previous number and adding 1 each time.

Identifying the pattern:
- The first number in the sequence, 3, belongs to the first sequence.
- The second number in the sequence, 1, belongs to the second sequence.
- The third number, 7, belongs to the first sequence.
- The fourth number, 3, belongs to the second sequence.
- The fifth number, 13, belongs to the first sequence.
- The sixth number, 7, belongs to the second sequence.
- The seventh number, 21, belongs to the first sequence.
- The eighth number, 15, belongs to the second sequence.
- The ninth number, 31, belongs to the first sequence.
- The tenth number, 31, belongs to the second sequence.

Continuing the pattern:
- We can observe that the first sequence increases by 4 each time, while the second sequence doubles the previous number and adds 1 each time.

Applying the pattern:
- To find the missing number, we need to determine which sequence it belongs to.
- The eleventh number, ?, should belong to the first sequence, as the previous number, 31, belongs to the second sequence.
- To find the eleventh number, we add 4 to the previous number in the first sequence: 31 + 4 = 35.

Final answer:
- The missing number in the sequence is 35.
- None of the given options (a) 41, (b) 39, (c) 38, (d) 43 match the correct answer, so the given options are incorrect.
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