An arithmetic sequence has first term $a$ and common difference $0.5$, where $a$ is an integer. Find

Question

An arithmetic sequence has first term $a$ and common difference $0.5$, where $a$ is an integer. Find the smallest value of $a$ such that the sum of the first $36$ terms is at least $500$. [3] A sequence ${{u}_{0}},\ {{u}_{1}},\ {{u}_{2}},\ \ldots $ is given by ${{u}_{0}}=400$ and ${{u}_{n}}=1.01{{u}_{n-1}}-x$ for $n\ge 1$, where $x$ is an integer. Show that ${{u}_{n}}={{1.01}^{n}}\left( 400 \right)-100x\left( {{1.01}^{n}}-1 \right)$. [3] Given that $x=16$ and $y=1.01{{u}_{k}}$, where $0 [4]

Accepted Answer

(a) $a=6$ (b)(i) $\displaystyle u_n=1.01^n(400)-100x(1.01^n-1)$ (b)(ii) $k=28$, $y=14.6\text{ (3 s.f.)}$

2024 CJC Promo Q8

2024 CJC Promo Q8

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