An infinite sequence is such that $u_1 = p$, where $p$ is a constant, and \(u_{n+1} =

Question

An infinite sequence is such that $u_1 = p$, where $p$ is a constant, and $u_{n+1} = 12 - \frac{24}{u_n}$, where $n \ge 1$. Showing your working clearly, explain why $p$ cannot be $2.4$.[2] A constant sequence is a sequence in which every term is the same. Given that $p > 5$, find the value of $p$ for which the sequence is a constant sequence.[2] An arithmetic series has a positive first term $v_1$ and common difference $d$. Given that $3v_{10} = 5v_{19}$, find the largest possible value of the sum of the first $n$ terms, leaving your answer in terms of $d$.[4]

Accepted Answer

(a)(i) $u_3=0$, so $u_4$ is undefined. (a)(ii) $p=6+2\sqrt3$ (b) Maximum sum $=-512d$, attained at $n=32$

2024 VJC Promo Q6

2024 VJC Promo Q6

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