Geometric Progressions

Arithmetic and Geometric Progressions Problem Solving


Let {an}\{a_n\} be a geometric progression such that a1+a3=15a_1+a_3=15 and a2+a4=30a_2+a_4=30. What is the sum of the first 55 terms of this geometric progression?

The sum of three numbers in geometric progression is 5252. If the product of the three numbers is 17281728, what is the value of the maximum number?

Let {an}\{a_n\} be a geometric progression such that a5=1516 and a8=15128.a_5=\frac{15}{16} \mbox{ and } a_8=\frac{15}{128}. What is the smallest integer nn for which an<0.001a_n < 0.001?

The curve y=x3+8x2+40xy=-x^3+8x^2+40x and the line y=ky=k intersect at 33 distinct points. If the xx-coordinates of these 33 points form a geometric progression, what is the real number k?k?

33 real numbers that form a geometric progression have sum equal to 175175 and product equal to 1757617576. What is the sum of the largest and smallest numbers?


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