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The-n-th-term-of-a-progression-is-np-q-and-the-sum-of-n-terms-is-denoted-by-S-n-Given-that-the-6-th-term-is-4-times-2-nd-term-and-that-S-3-12-find-the-value-of-p-and-q-Express-S-n-in-t




Question Number 11261 by 786786AM last updated on 18/Mar/17
The n^(th)  term of a progression is np+q and the sum of n terms is denoted by S_n .  Given that the 6^(th)  term is 4 times 2^(nd)  term and that S_3  =12, find the value of p and q.  Express S_n  in terms of n.
$$\mathrm{The}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{np}+\mathrm{q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{denoted}\:\mathrm{by}\:\mathrm{S}_{\mathrm{n}} . \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{6}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\mathrm{4}\:\mathrm{times}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{term}\:\mathrm{and}\:\mathrm{that}\:\mathrm{S}_{\mathrm{3}} \:=\mathrm{12},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$$$\mathrm{Express}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{n}. \\ $$

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