The sum of the first $n$ terms of a sequence, ${{S}_{n}}$, is given by \({{S}_{n}}=a{{n}^{3}}+b{

Question

The sum of the first $n$ terms of a sequence, ${{S}_{n}}$, is given by ${{S}_{n}}=a{{n}^{3}}+b{{n}^{2}}+cn+d$, where $a$, $b$, $c$ and $d$ are constants. It is given that ${{S}_{1}}=5$, ${{S}_{2}}=20$, ${{S}_{3}}=57$ and ${{S}_{4}}=128$. Find ${{S}_{n}}$.[4]

Accepted Answer

$a=2$, $b=-1$, $c=4$ and $d=0$. $\therefore S_n=2n^3-n^2+4n$

2023 SAJC Promo Q1

2023 SAJC Promo Q1

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