The sum, $S_n$, of the first $n$ terms of the sequence $u_1, u_2, u_3, \dots$ is given by \[S_

Question

The sum, $S_n$, of the first $n$ terms of the sequence $u_1, u_2, u_3, \dots$ 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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