List of practice Questions

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

Let a₁, a₂, a₃, … be a G.P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a₁a₉+a₂a₄ a₉+a₅+a₇ is equal to __________.

Let \( 0 < z < y < x \) be three real numbers such that \( \frac{1}{x}, \frac{1}{y}, \frac{1}{z} \) are in an arithmetic progression and \( x, \sqrt{2}y, z \) are in a geometric progression. If \( xy + yz + zx = \frac{3}{\sqrt{2}} xyz \), then \( 3(x + y + z)^2 \) is equal to ____________.

If an be the

n^{th}

term of the GP of positive numbers. Let

\sum_{n = 100}^{100} a_{2 n} = α

and

\sum_{n = 1}^{100} a_{2 n - 1} = β

such that

α \neq β

then the common ratio is:

Let,\(f(\theta)=\frac{sin^4\theta+3cos^2\theta}{sin^4\theta+cos^2\theta},\)then range of f(θ) ∈ [a, b]. The sum of infinite G.P., where first term is 64 and common ratio is a/b is equal to: