Discussion
The missing term in the following table
| x | f(x) |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 9 |
| 3 | - |
| 4 | 81 |
using difference operator method is :
Answer: D
The missing value is 31.
Five values are tabulated, with one missing, so we assume they lie on a polynomial of degree 3, whose fourth difference is zero:
\[ \begin{aligned} \Delta^{4} y_{0} &= y_{4} - 4y_{3} + 6y_{2} - 4y_{1} + y_{0} = 0 \\ 81 - 4y_{3} + 54 - 12 + 1 &= 0 \\ 124 - 4y_{3} &= 0 \\ y_{3} &= 31 \end{aligned} \]
The trap is that the given values 1, 3, 9, 81 suggest \(3^{x}\), which would put 27 in the gap. The difference-operator method does not assume an exponential; it fits the lowest-degree polynomial, and that gives 31, not 27, 28, 29 or 30.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development