In an arithmetic progression, the first term is \(a\) and the common difference is \(d\). The sum of the first three terms of this arithmetic progression is \(42\). The product of the first three terms of this arithmetic progression is \(-6720\).
Show that \(a(a+2d)=-480\).[3]
Hence, given that \(a\) is positive, find the values of \(a\) and \(d\).[4]
In a geometric progression, the \(3\)rd term is \(\dfrac{\mathrm{e}^{4x}}4\) and the \(10\)th term is \(\dfrac{\mathrm{e}^{11x}}{512}\). Find the first term and the common ratio.[5]
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Answer:(a)(i) \(a(a+2d)=-480\). (ii) \(a=40,\ d=-26\). (b) First term \(\mathrm{e}^{2x}\), common ratio \(\dfrac{\mathrm{e}^x}2\).