Question

The next term of the sequence 1 , 8 , 27 , 64 , 125 , ____.

• A. 343
• B. 325
• C. 256
• D. 216

Hint:

Familiarity with the perfect cubes of first 10 natural numbers is highly recommended:
\(1^3=1\), \(2^3=8\), \(3^3=27\), \(4^3=64\), \(5^3=125\), \(6^3=216\), \(7^3=343\).
Recognizing perfect cubes helps solve sequence problems instantly.

Answer 1

The Correct Option is D

Step 1: Identify the pattern in the sequence.
The sequence is 1, 8, 27, 64, 125. These are perfect cubes: 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125.
Step 2: Find the next term.
The next position is 6, so the next term = 6^3 = 6 x 6 x 6 = 216.
Step 3: Verify.
The cubic sequence continues as 1, 8, 27, 64, 125, 216, 343, ... confirming the answer.
\[ \boxed{216} \]