If $${3^{2\sin 2\alpha - 1}}$$, 14 and $${3^{4 - 2\sin 2\alpha }}$$ are the first three terms of an A.P. for some $$\alpha $$, then the sixth terms of this A.P. is:

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: