CAT 2021 Slot 1 · Quant · Question 14
CAT 2021 Slot 1 previous year question on Sequences and Series, with the answer and a step-by-step solution.
If {x}_{0}=1, {x}_{1}=2 and {x}_{n+2}=\frac{1+{x}_{n+1}}{{x}_{n}} for n=0,1,2,3,\ldots, then {x}_{2021} is equal to
- A1
- B2
- C3
- D4
Pick an option, then check.
Answer & solution
Answer: Option B
Computing successive terms, {x}_{2}=3, {x}_{3}=2, {x}_{4}=1, {x}_{5}=1, {x}_{6}=2 and {x}_{7}=3, so the sequence repeats with period 5.
Since 2021=5\times 404+1, {x}_{2021}={x}_{1}=2.
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