Let a₁, a₂, ..........., a₂₁ be an AP such that $$\sum\limits_{n = 1}^{20} {{1 \over {{a_n}{a_{n + 1}}}} = {4 \over 9}} $$. If the sum of this AP is 189, then a₆a₁₆ is equal to :

Let a₁, a₂, a₃, ..... be an A.P. If $${{{a_1} + {a_2} + .... + {a_{10}}} \over {{a_1} + {a_2} + .... + {a_p}}} = {{100} \over {{p^2}}}$$, p $$\ne$$ 10, then $${{{a_{11}}} \over {{a_{10}}}}$$ is equal to :

The sum of 10 terms of the series

$${3 \over {{1^2} \times {2^2}}} + {5 \over {{2^2} \times {3^2}}} + {7 \over {{3^2} \times {4^2}}} + ....$$ is :

Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3 r², then r² $$-$$ d is equal to :