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Question Number 11261 by 786786AM last updated on 18/Mar/17

$$\mathrm{The}{\mathrm{n}}^{\mathrm{th}}\mathrm{term}\mathrm{of}\mathrm{a}\mathrm{progression}\mathrm{is}\mathrm{np}+\mathrm{q}\mathrm{and}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{n}\mathrm{terms}\mathrm{is}\mathrm{denoted}\mathrm{by}{\mathrm{S}}_{\mathrm{n}}.$$$$\mathrm{Given}\mathrm{that}\mathrm{the}{6}^{\mathrm{th}}\mathrm{term}\mathrm{is}4\mathrm{times}{2}^{\mathrm{nd}}\mathrm{term}\mathrm{and}\mathrm{that}{\mathrm{S}}_3=12,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{p}\mathrm{and}\mathrm{q}.$$$$\mathrm{Express}{\mathrm{S}}_{\mathrm{n}}\mathrm{in}\mathrm{terms}\mathrm{of}\mathrm{n}.$$

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