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Question

What will come in place of * in the sequence 3, 14, 39, 84, *, 258?

The correct answer is

155

Given series: 3, 14, 39, 84, *, 258

The series follows the following pattern:

\[ 1^3 + 1^2 + 1 = 3 \]

\[ 2^3 + 2^2 + 2 = 14 \]

\[ 3^3 + 3^2 + 3 = 39 \]

\[ 4^3 + 4^2 + 4 = 84 \]

Next term:

\[ * = 5^3 + 5^2 + 5 = 155 \]

Final term:

\[ 6^3 + 6^2 + 6 = 258 \]

Conclusion: The missing number is 155.

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