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CAT Exam 2021 Slot 1 Solved Paper

Question : 62 of 66

Marks: +1, -0

x^0=1, x^1=2,

x^{n+2}=\frac{1+x^{n+1}}{x^n}

n=0,1,2,3,\ldots

x^{2021}

is equal to

Solution:

x^0=1

x^1=2

x^2=\frac{1+x^1}{x^0}=\frac{1+2}{1}=3

x^3=\frac{1+x^2}{x1}=\frac{1+3}{2}=2

x^4=\frac{1+x^3}{x^2}=\frac{1+2}{3}=1

x^5=\frac{1+x^4}{x^3}=\frac{1+1}{2}=1

x^6=\frac{1+x^5}{x^4}=\frac{1+1}{1}=2

Hence, the series begins to repeat itself after every 5 terms. Terms whose number is of the form 5n are

1, 5n+1

are 2... and so on, where

n=0,1,2,3,\ldots

2021 is of the form

5n+1

Hence, its value will be 2.

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