Thriving Scholars TMUA Full Mock Test 1 Paper 1 · Question 15

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Thriving Scholars TMUA Full Mock Test 1 Paper 1 · Q15

Paper 1Sequences & seriesNumber & counting

A sequence of numbers is defined recursively by $a_1=1$ , $a_2=\dfrac37$ , and

a_n=\frac{a_{n-2}\cdot a_{n-1}}{2a_{n-2}-a_{n-1}}

for all $n\ge3$ . Then $a_{2019}$ can be written as $\dfrac pq$ , where $p$ and $q$ are relatively prime positive integers. What is $p+q$ ?

2020

4039

6057

6061

8078

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