Find out the missing number in the following sequence: 1,3,3,6,7,9, ?, 12, 21
Step-by-step Solution:
We analyze the given sequence step-by-step:\[\] \[\] Step 1: Look at the pattern of the sequence\[\] Notice that the sequence alternates between adding 2 and performing other operations.\[\] The sequence breaks into two alternating subsequences:\[\] Odd Positions: (1, 3, 7, ?) Even Positions: (3, 6, 9, 12, 21) \[\] \[\] Analyze Odd Positions: 1. 1, 3, 7 - Increasing by (+2, +4). The next number follows a pattern of adding increasing even numbers. 1 + 2 = 3, \quad 3 + 4 = 7 \[\] 2. The next number would add (6) (the next even number in the sequence). 7 + 6 = 13 \[\] So, the missing number is 13.\[\] \[\] Final Answer:\[\] The missing number is: 13[\] \[\] Correct Option: (d)