Exams › GATE › Engineering Mathematics
A series of natural numbers F1, F2, F3, F4, F5, F6, F7,... obeys Fₙ₊₁ = Fₙ + Fₙ₋₁ for all integers n ≥ 2. If F6 = 37, and F7 = 60, then what is F1 ?
- 4
- 5
- 8
- 9
Correct answer: 4
Solution
The sequence follows the Fibonacci-like relation where each term is the sum of the two preceding terms. Given F6 = 37 and F7 = 60, we can work backwards to find F5 = F7 - F6 = 60 - 37 = 23, then F4 = F5 - F6 = 23 - 37 = -14, and continuing this process leads us to F1 = 4.
Related GATE Engineering Mathematics questions
- What are the eigenvalues of the matrix [2, 1, 1; 1, 4, 1; 1, 1, 2]?
- A circle with center at (x,y) = (0.5, 0) and radius = 0.5 intersects with another circle with center at (x,y) = (1,1) and radius = 1 at two points. One of the points of intersection (x,y) is:
- Suppose λ is an eigenvalue of matrix A and x is the corresponding eigenvector. Let x also be an eigenvector of the matrix B = A − 2I, where I is the identity matrix. Then, the eigenvalue of B corresponding to the eigenvector x is equal to
- Let A = [[1, 1], [1, 3], [−2, −3]] and b = [b1, b2, b3]. For Ax = b to be solvable, which one of the following options is the correct condition on b1, b2, and b3:
- If the quadrantal bearing of a line is N 30° W, then the whole circle bearing of the line is
- The matrix [2, -4; 4, -2] has
⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →