The sum, ${{S}_{n}}$, of the first $n$ terms of an arithmetic progression is given by ${{S}_{n}}=pn+

Question

The sum, ${{S}_{n}}$, of the first $n$ terms of an arithmetic progression is given by ${{S}_{n}}=pn+q{{n}^{2}}$. Given also that ${{S}_{3}}=6$ and ${{S}_{5}}=11$, Find the values of $p$ and $q$. [3] Deduce, or find otherwise, an expression for the $n$-th term and the value of the common difference. [3] Find the set of values of $	heta $ lying in the interval $-\frac{1}{2}\pi [4]

Accepted Answer

(a)(i) $p = \frac{17}{10}$, $q = \frac{1}{10}$ (a)(ii) $u_n = \frac{1}{5}n + \frac{8}{5}$, $d = \frac{1}{5}$ (b) $\left\{\theta \in \mathbb{R}: 0.524 < \theta < \frac{\pi}{2}\right\}$

N1984 P1 Q1

N1984 P1 Q1

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