Geometric Progression (GP): JEE Questions & Solutions

Let a1, a2, a3, be a G.P. of increasing positive terms such that a2 a3 a4=64 and a1 + a3 + a5 = 8137. Then a3 + a5 + a7 is equal to:

Let a1, a22, a32^2,, a102^9 be a G.P. of common ratio 1 2. If a1 + a2 + + a10 = 62, then a1 is equal to:

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R -…

Let a1, a2, a3, be a G.P. of increasing positive terms. If a1 a5 = 28 and a2 + a4 = 29, then the value of a6 is equal to:

Let a1, a2, a3,... be a G.P. of increasing positive numbers. If a3 a5 = 729 and a2 + a4 = 1114, then 24(a1 + a2 + a3) is equal to

Let x1, x2, x3, x4 be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from x1, x2, x3, x4, then the resulting numbers…

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is…

If in a G.P. of 64 terms, the sum of all terms is 7 times the sum of the odd terms, then the common ratio of the G.P. is equal to:

If each term of a geometric progression a1, a2, a3, with a1 = 18 and a2 a1, is the arithmetic mean of the next two terms and Sn = a1 + a2 +…

Let a and b be distinct positive real numbers. The 11th term of a GP (first term a, third term b) equals the pth term of another GP (first…

Let a, ar, ar^2,... be an infinite G.P. If n=0^ ar^n = 57 and n=0^ a^3r^3n = 9747, then a + 18r is equal to:

Let a, ar, ar^2, be an infinite G.P. If n=0^ ar^n = 57 and n=0^ a^3r^3n = 9747, then a + 18r is equal to:

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 70 3 and the product of the third and…

For the two positive numbers a, b, if a, b and 118 are in a geometric progression, while 1a, 10, 1b are in an arithmetic progression, then…

Let a1, a2, a3, be a geometric progression (GP) of increasing positive numbers. If the product of the fourth and sixth terms is 9 and the…

Let ak and bk, k N, be two G.P.s with common ratios r1 and r2, respectively, such that a1 = b1 = 4 and r1 < r2. Let ck = ak + bk, k N. If…

The parabolas: ax^2 + 2bx + cy = 0 and dx^2 + 2ex + fy = 0 intersect on the line y = 1. If a, b, c, d, e, f are positive real numbers and…

If the sum and product of four positive consecutive terms of a G.P. are 126 and 1296, respectively, then the sum of common ratios of all…

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms…

Suppose a1, a2, a3, a4 be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression in 2 and…

Let S = 109 + 1085 + 1075^2 + 1065^3 +. Then the value of (16S - (25)^3) is equal to:

Let a1, a2, a3, be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th…

Let A1 and A2 be two arithmetic means and G1, G2, G3 be three geometric means of two distinct positive numbers. Then…