NIMCET 2009 — Reasoning PYQ

Step 1: Analyze the pattern between terms

• 1st to 2nd term:

  $12\times 2-2=22$

• 2nd to 3rd term:

  $22\times 3+3=69$

• 3rd to 4th term:

  $69\times 4-4=272$

• 4th to 5th term:

  $272\times 5+5=1365$

Step 2: Identify the general rule

The pattern follows a sequence of multiplying by $n$ and then alternatively subtracting and adding $n$, where $n$ increases by 1 for each step starting from 2.

The logic is: ${\text{Term}}_n=({\text{Term}}_{n-1}\times n)\pm n$.

Step 3: Calculate the missing term (?)

Following the established pattern, the next multiplier and operator will be $\times 6$ and $-6$:

Final Answer:

The missing number in the series is 8184.

Correct Option: (d)