If 1+(1–2².1)+(1–4².3)+(1-6².5)+......+(1-20².19)= $$\alpha $$ - 220$$\beta $$,
then an ordered pair $$\left( {\alpha ,\beta } \right)$$ is equal to:

If the sum of the series

20 + 19$${3 \over 5}$$ + 19$${1 \over 5}$$ + 18$${4 \over 5}$$ + ...

upto nth term is 488 and the n^th term is negative, then :

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :

Let S be the sum of the first 9 terms of the series :
{x + k$$a$$} + {x² + (k + 2)$$a$$} + {x³ + (k + 4)$$a$$}
+ {x⁴ + (k + 6)$$a$$} + .... where a $$ \ne $$ 0 and x $$ \ne $$ 1.

If S = $${{{x^{10}} - x + 45a\left( {x - 1} \right)} \over {x - 1}}$$, then k is equal to :