CUET PG 2021 — Reasoning PYQ

1. Identify the Interleaved Sequences

The sequence can be split into numbers at even positions and numbers at odd positions.

• Sequence 1 (Even positions): $3,6,9,12,\dots$

• Sequence 2 (Odd positions): $1,3,7,?,21$

2. Analyze Sequence 1 (Even Positions)

This is a simple arithmetic progression where $3$ is added to each term:

3. Analyze Sequence 2 (Odd Positions)

This sequence follows a pattern where the difference between consecutive terms increases by $2$ each time ($+2,+4,+6,+8$).

• First term: $1$

• Second term: $1+2=3$

• Third term: $3+4=7$

• Fourth term (Missing Number): $7+6=13$

• Fifth term: $13+8=21$

The pattern of differences is:

4. Calculation of the Missing Number

The missing number is the fourth term of the odd-positioned sequence:

Final Answer:

The missing number in the sequence is $13$.