The minimum value of 2^sinx + 2^cosx is :

Let a₁, a₂, ..., an be a given A.P. whose
common difference is an integer and
S_n = a₁ + a₂ + .... + a_n. If a₁ = 1, a_n = 300 and 15 $$ \le $$ n $$ \le $$ 50, then
the ordered pair (S_n-4, a_n–4) is equal to:

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 :