Find the next term in the given series 9, 54, 135, 252,?

Explanation: Determine the pattern by examining differences between consecutive terms.

• Step 1: Compute consecutive differences: 54 − 9 = 45, 135 − 54 = 81, 252 − 135 = 117.

• Step 2: Notice the differences form an arithmetic sequence increasing by 36: 81 − 45 = 36 and 117 − 81 = 36. So the next difference is 117 + 36 = 153.

• Step 3: Add the next difference to the last term: 252 + 153 = 405.

Therefore the next term in the series is 405.