Official PYQ · 2023Q3MCQ1 mark

GATE CS 2023 Q3 — General Aptitude

A series of natural numbers $F_1, F_2, F_3, F_4, F_5, F_6, F_7, \ldots$ obeys $F_{n+1}=F_n+F_{n-1}$ for all integers $n \geq 2$ .

If $F_6=37,$ and $F_7=60,$ then what is $F_1 ?$

View worked solution

Answer: A

The given recurrence relation is:

F_{n+1} = F_n + F_{n-1} \quad \text{for } n \geq 2

We can rewrite this relation to find the previous term in the sequence:

F_{n-1} = F_{n+1} - F_n

We are given $F_7 = 60$ and $F_6 = 37$ . Let us work backwards to find $F_1$ :

For $n = 6$ :
$F_5 = F_7 - F_6 = 60 - 37 = 23$
For $n = 5$ :
$F_4 = F_6 - F_5 = 37 - 23 = 14$
For $n = 4$ :
$F_3 = F_5 - F_4 = 23 - 14 = 9$
For $n = 3$ :
$F_2 = F_4 - F_3 = 14 - 9 = 5$
For $n = 2$ :
$F_1 = F_3 - F_2 = 9 - 5 = 4$

Thus, the value of $F_1$ is 4.

Free practice · Your answers on this page are not saved.

Published 10 Oct 2026

Report a correction

GATE CS · 2026
For positive real numbers $S$ and $K$ , the function $H_{K}(S)$ is defined as: $H_{K}(S)=\max (S-K, 0)$ . The max function is defined as: $\max (a, b)=\left\{\begin{array}{ll} a, & \text{ when } a>b \\ b, & \text{ when } a \leq b \end{array}\right.$ The graph below shows the plot of a function $N(S)$ versus $S$ . $N(S)$ can be …
MCQ · 2 marks
GATE CS · 2026
An unbiased six-faced dice whose faces are marked with numbers $1,2,3,4,5$ , and $6$ is rolled twice in succession and the number on the top face is recorded each time. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is $\_\_\_\_$
MCQ · 2 marks
GATE CS · 2026
A day can only be cloudy or sunny. The probability of a day being cloudy is $0.5$ , independent of the condition on other days. What is the probability that in any given four days, there will be three cloudy days and one sunny day?
MCQ · 1 mark
GATE CS · 2026
The values of Stock $\text{A}$ and Stock $\text{B}$ on a particular day are Rs. $50$ and Rs. $80$ , respectively. An investor invests Rs. $100$ in Stock $\text{A}$ and Rs. $80$ in Stock $\text{B}$ . He sells all the stocks the next day when the value of Stock $\text{A}$ is Rs. $55$ and Stock $\text{B}$ is Rs. $70$ . The profit made by …
MCQ · 1 mark
GATE CS · 2026
Figures $\text{(i)}$ and $\text{(ii)}$ represent intercity highway systems. The black dots represent cities and the line segments between them represent intercity highways. A salesperson needs to make a trip. She needs to start from a city, visit each of the remaining cities exactly once, and finally return to the same city from which she started. Which …
MCQ · 2 marks
GATE CS · 2026
An unbiased six-faced dice whose faces are marked with numbers $1,2,3,4,5$ , and $6$ is rolled twice in succession and the number on the top face is recorded each time. The probability that the sum of the two recorded numbers is a prime number is $\_\_\_\_\_\_\_$
MCQ · 2 marks

Browse this subject

More General Aptitude questions

GATE CS 2023 Q3 — General Aptitude

Related questions