Algebra Sequences Mock Tests

The sum of the series 1 + 2x + 3x^2 + 4x^3 + ... to infinity, where |x| < 1, is

The first and second terms of a geometric progression (GP) are 4 and 8 respectively. If an arithmetic progression (AP) has the same first term and common difference equal to the common ratio of the GP, then the sum of the first five terms of the AP is:

An arithmetic progression has first term a and common difference d. If the sum of the first 3 terms is 33 and the sum of the next 3 terms is 51, then the 10th term is

The sum of the series 1 + 3x + 5x^2 + 7x^3 + ... up to n terms, where |x| < 1, is

Let a₁, a₂, ..., a₁₀ be an arithmetic progression with a₁ = 1 and a₁₀ = 28. Let b₁, b₂, ..., b₁₀ be a geometric progression with b₁ = 1 and b₁₀ = 512. If cₖ = aₖ + bₖ for k = 1, 2, ..., 10, then the value of sum of cₖ is:

Let a₁, a₂, ..., aₙ be an arithmetic progression with a₁ = 2 and common difference d > 0. If a₃ = a₁ + a₂, then the sum of the first 6 terms is:

Let a1, a2, a3, ... be an arithmetic progression with a1 = 1 and a4 = 7. Let b1, b2, b3, ... be a geometric progression with b1 = 1 and b3 = 9. If cn = an · bn for all n >= 1, then the sum a1b1 + a2b2 + a3b3 + ... + a10b10 is equal to: