Question

Find the next number in the series: 2, 5, 14, 41, 122, ? , 1094

• A. 360
• B. 364
• C. 365
• D. 366

Hint:

Whenever differences form a geometric progression \((3,9,27,81,\ldots)\), check for a multiplication-based recurrence relation.

Answer 1

The Correct Option is C

Step 1: Identify the operation between consecutive terms.
\[ 2\times3-1=5 \] \[ 5\times3-1=14 \] \[ 14\times3-1=41 \] \[ 41\times3-1=122 \] Thus the rule is: \[ a_{n+1}=3a_n-1 \]

Step 2: Apply the rule to the last term.
\[ 122\times3-1=366-1=365 \] Therefore, the next term is {365}