If the sum of an infinite GP a, ar, ar², ar³, ....... is 15 and the sum of the squares of its each term is 150, then the sum of ar², ar⁴, ar⁶, ....... is :

Let S_n be the sum of the first n terms of an arithmetic progression. If S_3n = 3S_2n, then the value of $${{{S_{4n}}} \over {{S_{2n}}}}$$ is :

Let S_n denote the sum of first n-terms of an arithmetic progression. If S₁₀ = 530, S₅ = 140, then S₂₀ $$-$$ S₆ is equal to:

If sum of the first 21 terms of the series $${\log _{{9^{1/2}}}}x + {\log _{{9^{1/3}}}}x + {\log _{{9^{1/4}}}}x + .......$$, where x > 0 is 504, then x is equal to