(A) To climb a staircase of $n$ steps,the person can either take a single step from the $(n-1)$-th step or a double step from the $(n-2)$-th step.This

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) To climb a staircase of $n$ steps,the person can either take a single step from the $(n-1)$-th step or a double step from the $(n-2)$-th step.This gives the recurrence relation: $C_n = C_{n-1} + C_{n-2}$ for $n > 2$.This is the definition of the Fibonacci sequence.Given the relation $C_n = C_{n-1} + C_{n-2}$,we can substitute $n = 20$ into the formula.Thus,$C_{20} = C_{19} + C_{18}$.Therefore,$C_{18} + C_{19} = C_{20}$.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

Medium

$A$ person wants to climb a $n$-step staircase using one step or two steps. Let $C_n$ denote the number of ways of climbing the $n$-step staircase. Then $C_{18} + C_{19}$ equals

A
$C_{20}$
B
$C_{21}$
C
greater than $C_{21}$
D
less than $C_{20}$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Permutation and Combination

Subtopic

Permutation and Combination

The number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is

Medium

View Solution

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

Difficult

View Solution

How many different words can be formed with the letters of the word '$BHARAT$'? In how many of these are $B$ and $H$ never together?

Medium

View Solution

How many words,each of $3$ vowels and $2$ consonants,can be formed from the letters of the word '$INVOLUTE$'?

Difficult

View Solution

In how many different ways can the letters of the word '$JUDGE$' be arranged in such a way that the vowels always come together?

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ person wants to climb a $n$-step staircase using one step or two steps. Let $C_n$ denote the number of ways of climbing the $n$-step staircase. Then $C_{18} + C_{19}$ equals

Similar Questions

The number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

How many different words can be formed with the letters of the word '$BHARAT$'? In how many of these are $B$ and $H$ never together?

How many words,each of $3$ vowels and $2$ consonants,can be formed from the letters of the word '$INVOLUTE$'?

In how many different ways can the letters of the word '$JUDGE$' be arranged in such a way that the vowels always come together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module