Bodhee Prep-CAT Online Preparation

| Best Online CAT PreparationFor Enquiry CALL @ +91-95189-40261

# CAT 2021 Quant Question [Slot 1] with Solution 18

Question
If ${x_0} = 1,{x_1} = 2$, and ${x_{n + 2}} = \frac{{1 + {x_{n + 1}}}}{{{x_n}}},n = 0,1,2,3,......,$ then ${x_{2021}}$ is equal to
1. 4
2. 1
3. 3
4. 2
Option: 4
Solution:
${x_0} = 1$
${x_1} = 2$
${x_2} = \frac{{\left( {1 + {x_1}} \right)}}{{{x_0}}} = \frac{{\left( {1 + 2} \right)}}{1} = 3$
${x_3} = \frac{{\left( {1 + {x_2}} \right)}}{{{x_1}}} = \frac{{\left( {1 + 3} \right)}}{2} = 2$
${x_4} = \frac{{\left( {1 + {x_3}} \right)}}{{{x_2}}} = \frac{{\left( {1 + 2} \right)}}{3} = 1$
${x_5} = \frac{{\left( {1 + {x_4}} \right)}}{{{x_3}}} = \frac{{\left( {1 + 1} \right)}}{2} = 1$
${x_6} = \frac{{\left( {1 + {x_5}} \right)}}{{{x_4}}} = \frac{{\left( {1 + 1} \right)}}{1} = 2$
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,....
2021 is of the form 5n+1. Hence, its value will be 2.
CAT Online Course @ INR 9999 only

## CAT 2021 Quant questions with Solutions

### CAT 2023Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon