CAT Exam Model Paper 4 with solutions for free online practice

Question : 8 of 60

Marks: +1, -0

a _ { 1 } = 1 , a _ { 2 } = 2

and

a _ { n + 2 } = a _ { n } ( a _ { n +1} , - 1 )

, where n is a natural number. What is the value of a

_{1000}

Solution:

a _ { 1 } = 1

a _ { 2 } = 2

a _ { 3 } = 1 ( 1 ) = 1

a _ { 4 } = 2 ( 0 ) = 0

a _ { 5 } = 1 ( - 1 ) = - 1

a _ { 6 } = 0 ( - 2 ) = 0

a _ { 7 } = - 1 ( - 1 ) = 1

a _ { 8 } = 0 ( 0 ) = 0

a _ { 9 } = 1 ( - 1 ) = - 1

After

a _ { 1 } \and a _ { 2 }

, there is a cyclicity of ‘4' in the remaining terms

a _ { 1000 } = a _ { 2 + 4 ×249 + 2 } = 0

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