Explanation:
To find out the wrong term in the number series, we need to observe the pattern and logic behind the given numbers.

Pattern in the series:
Let's analyze the given series step by step:
1. The first term is 2.
2. The second term is obtained by multiplying the first term by 3: 2 x 3 = 6.
3. The third term is obtained by multiplying the second term by 3: 6 x 3 = 18.
4. The fourth term is obtained by adding the square of the previous term to the product of the previous term and 5, i.e., (18)^2 + 18 x 5 = 324 + 90 = 414.
5. The fifth term is obtained by adding the square of the previous term to the product of the previous term and 10, i.e., (414)^2 + 414 x 10 = 171396 + 4140 = 175536.

Identifying the wrong term:
Comparing the pattern with the given series, we can see that all the terms except the fourth term (82) and fifth term (650) follow the pattern. Hence, either the fourth term or the fifth term is the wrong term in the series.

Comparison of the fourth and fifth terms:
1. The fourth term, 82, is obtained using the formula (18)^2 + 18 x 5 = 414.
2. The fifth term, 650, is obtained using the formula (414)^2 + 414 x 10 = 175536.

Conclusion:
Since the fifth term (650) does not follow the pattern of the series, it is the wrong term in the given number series.

Wrong term:
The wrong term in the series is 650.

Corrected series:
The corrected series would be 2, 6, 18, 82, 414.

This is wrong. (3) 82 .