C. A sequence (a_n) has the property that a_{n+1}=\frac{a_n}{a_{n-1}} for every n \geq 2. Given that a_1=2 and a_2=6, what is a_{2017} ?

Oxford University MAT 2017 Solved Papers

Question : 3 of 10

Marks: +1, -0

C. A sequence

(a_n)

has the property that

a_{n+1}=\;{a_n}/{a_{n-1}}

for every

n ≥ 2

. Given that

a_1=2

and

a_2=6

, what is

a_{2017}

Solution:

Calculating the first few terms gives the pattern

2,6,3, \;{1}/{2}, \;{1}/{6}, \;{1}/{3}, 2,6, . . .

The sequence repeats every six terms, and 2017 divided by 6 leaves remainder 1 . Hence the answer is

( {d})

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