The sum, $S_n$, of the first $n$ terms of a sequence $u_1,u_2,u_3,\ldots$ is given by \(S_n=a\

Question

The sum, $S_n$, of the first $n$ terms of a sequence $u_1,u_2,u_3,\ldots$ is given by $S_n=a\left(1-\dfrac{1}{n}\right)+bn+c$, where $a$, $b$ and $c$ are constants. State the condition on $b$ for $S_n$ to converge and find the sum to infinity.[2] Find $u_1$ and $u_n$ for $n\geq2$, leaving your answers in terms of $a$, $b$ or $c$.[3] Given that $u_1=2$, $u_2=6$ and $S_4=\dfrac{37}{2}$, find $a$, $b$ and $c$.[3]

Accepted Answer

(a) $b=0,\ S_\infty=a+c$ (b) $u_1=b+c,\ u_n=\dfrac{a}{n(n-1)}+b$ for $n\geq2$ (c) $a=2,\ b=5,\ c=-3$.

2026 HCI Promo Q3

2026 HCI Promo Q3

Solution:

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