A sequence is such that $u_1 = N$ where $N$ is a constant, and $u_{n+1} = 3u_n - 8$,

Question

A sequence is such that $u_1 = N$ where $N$ is a constant, and $u_{n+1} = 3u_n - 8$, for $n \ge 1$. Describe how the sequence behaves when $N = 4$,[1] $N = 3$.[1] Find the value of $N$ for which $u_5 = 409$.[2] The sequence $v_n = (-1)^n (u_n + k)$ for $n \ge 1$ where $k$ is a constant, is convergent when $u_1 = 4$. State the value of $k$.[1]

Accepted Answer

(a)(i) Constant at $4$ (ii) Strictly decreasing and divergent to $-\infty$ (b) $N=9$ (c) $k=-4$

2025 RVHS P2 Q1

2025 RVHS P2 Q1

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