If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is :

Let A₁, A₂, A₃, ....... be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = $${1 \over {1296}}$$ and A₂ + A₄ = $${7 \over {36}}$$, then the value of A₆ + A₈ + A₁₀ is equal to

Let $$S = 2 + {6 \over 7} + {{12} \over {{7^2}}} + {{20} \over {{7^3}}} + {{30} \over {{7^4}}} + \,.....$$. Then 4S is equal to

If a₁, a₂, a₃ ...... and b₁, b₂, b₃ ....... are A.P., and a₁ = 2, a₁₀ = 3, a₁b₁ = 1 = a₁₀b₁₀, then a₄ b₄ is equal to -