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

EXPLANATION

Correct Option (2)

The given sequence follows a specific mathematical pattern where each term is derived from the formula $n^{3} + n^{2} + n$ , where $n$ represents the position of the term in the sequence.

For the 1st term ( $n = 1$ ): $1^{3} + 1^{2} + 1 = 1 + 1 + 1 = 3$
For the 2nd term ( $n = 2$ ): $2^{3} + 2^{2} + 2 = 8 + 4 + 2 = 14$
For the 3rd term ( $n = 3$ ): $3^{3} + 3^{2} + 3 = 27 + 9 + 3 = 39$
For the 4th term ( $n = 4$ ): $4^{3} + 4^{2} + 4 = 64 + 16 + 4 = 84$
To find the missing 5th term ( $n = 5$ ): $5^{3} + 5^{2} + 5 = 125 + 25 + 5 = 155$
For the 6th term ( $n = 6$ ): $6^{3} + 6^{2} + 6 = 216 + 36 + 6 = 258$

Therefore, the missing term in the sequence is 155.

Incorrect Options:

Options 150, 160, and 176 are incorrect as they do not conform to the established mathematical pattern of $n^{3} + n^{2} + n$ that governs the given sequence.