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

Let S₁ be the sum of first 2n terms of an arithmetic progression. Let S₂ be the sum of first 4n terms of the same arithmetic progression. If (S₂ $$-$$ S₁) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :

If $$\alpha$$, $$\beta$$ are natural numbers such that
100^$$\alpha$$ $$-$$ 199$$\beta$$ = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through ($$\alpha$$, $$\beta$$) and origin is :