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

Step 1: Look at the first term as two pieces.
Read $28$ as the digit $2$ followed by $8$, and notice $8 = 2^{3}$.
Step 2: Test the second term.
$327$ splits as $3$ then $27$, and $27 = 3^{3}$. The same rule holds.
Step 3: Test the third term.
$464$ splits as $4$ then $64$, and $64 = 4^{3}$. Still consistent.
Step 4: Test the fourth term.
$5125$ splits as $5$ then $125$, and $125 = 5^{3}$. The pattern is confirmed.
Step 5: State the rule.
Each term is the number $n$ written next to its cube $n^{3}$.
Step 6: Apply it to $n = 6$.
$6^{3} = 216$, so the next term is $6$ followed by $216$, namely $6216$.
\[ \boxed{6216} \]