The sum, ${{S}_{n}}$, of the first $n$ terms of the sequence ${{u}_{1}}$, ${{u}_{2}}$, \({{u

Question

The sum, ${{S}_{n}}$, of the first $n$ terms of the sequence ${{u}_{1}}$, ${{u}_{2}}$, ${{u}_{3}}$, $\ldots $ is given by ${{S}_{n}}={{n}^{2}}+kn$, where $k$ is a non-zero constant. Find ${{u}_{n}}$ in terms of $n$ and $k$.[2] Hence determine if the sequence is an arithmetic progression.[2]

Accepted Answer

(i) $u_n=2n-1+k$. (ii) Yes; it is an arithmetic progression with common difference $2$.

2024 MI PRU1 P1 Q1

2024 MI PRU1 P1 Q1

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