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 = 813/7. Then a₃ + a₅ + a₇ is equal to:

Let a₁, a₂/2, a₃/2², …, a₁₀/2⁹ 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 = 111/4, 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 = 1/8 and a₂ ≠ a₁, is the arithmetic mean of the next two terms and Sₙ = a₁ +…

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, ar², … be an infinite G.P. If Σ_(n=0)^∞ arⁿ = 57 and Σ_(n=0)^∞ a³r³ⁿ = 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 1/18 are in a geometric progression, while 1/a, 10, 1/b are in an arithmetic progression,…

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 {a_k} and {b_k}, k ∈ ℕ, be two G.P.s with common ratios r₁ and r₂ respectively, such that a₁ = b₁ = 4 and r₁ < r₂. Let c_k = a_k + b_k,…

The parabolas: ax² + 2bx + cy = 0 and dx² + 2ex + fy = 0 intersect on the line y = 1. If a, b, c, d, e, f are positive real numbers and a,…

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

Let S = 109 + 108/5 + 107/5² + 106/5³ + … + 2/5¹⁰⁷ + 1/5¹⁰⁸. Then the value of (16S - (25)⁻⁵⁴) 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 G₁⁴+G₂⁴+G₃⁴+G₁²G₃² is…