Question

Find the next term in the following sequence: \[ 28,\;327,\;464,\;5125,\;? \]

• A. 6125
• B. 6216
• C. 7216
• D. 6126

Hint:

Whenever a sequence contains numbers such as \(27,64,125,216\), always check cubes: \[ 3^3,4^3,5^3,6^3 \]

Answer 1

The Correct Option is B

Concept: Observe the pattern carefully. \[ 28 = 2^3 \] represented as \[ 2,\;8 \] Similarly, \[ 327 = 3^3=27 \] represented as \[ 3,\;27 \] \[ 464 = 4^3=64 \] represented as \[ 4,\;64 \] \[ 5125 = 5^3=125 \] represented as \[ 5,\;125 \]

Step 1: Identify the rule.
Each term is formed by writing: \[ n \quad \text{followed by} \quad n^3 \]

Step 2: Apply the rule for the next number.
For \[ n=6 \] \[ 6^3=216 \] Thus the next term is \[ 6216 \] \[ \boxed{6216} \] Hence option (B) is correct.