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A geometric progression is a sequence of numbers where the previous term is multiplied by a constant to get the next term. 1, 2, 4, 8,... is a geometric sequence where each term is multiplied by 2.
Let \(\{a_n\}\) be a geometric progression such that \(a_1+a_3=15\) and \(a_2+a_4=30\). What is the sum of the first \(5\) terms of this geometric progression?
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The sum of three numbers in geometric progression is \(52\). If the product of the three numbers is \(1728\), what is the value of the maximum number?
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Let \(\{a_n\}\) be a geometric progression such that \[a_5=\frac{15}{16} \mbox{ and } a_8=\frac{15}{128}.\] What is the smallest integer \(n\) for which \(a_n < 0.001\)?
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The curve \(y=-x^3+8x^2+40x\) and the line \(y=k\) intersect at \(3\) distinct points. If the \(x\)-coordinates of these \(3\) points form a geometric progression, what is the real number \(k?\)
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\(3\) real numbers that form a geometric progression have sum equal to \(175\) and product equal to \(17576\). What is the sum of the largest and smallest numbers?
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