The sum, ${{S}_{n}}$, of the first $n$ terms of a series is given by ${{S}_{n}}={{n}^{2}}+2n$.

Question

The sum, ${{S}_{n}}$, of the first $n$ terms of a series is given by ${{S}_{n}}={{n}^{2}}+2n$. Show that this is an arithmetic series. Find the values of the first term and the common difference.[4] In a geometric progression, the first term is $12$ and the sixth term is $-\frac{3}{8}$. Let the sum of the first $n$ terms of the progression and the sum to infinity be ${{S}_{n}}$ and $S$ respectively. Find the least value of $n$ for which the difference between ${{S}_{n}}$ and $S$ is less than $0.001$.)[4]

Accepted Answer

(a) $a=3$, $d=2$ (b) $n=13$

2024 NYJC Promo Q6

2024 NYJC Promo Q6

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