If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

The sum of the first four terms is $$S_4 = \frac{4}{2}(2 \times 3 + 3d) = 2(6 + 3d) = 12 + 6d$$. 

The sum of the first eight terms is $$S_8 = \frac{8}{2}(2 \times 3 + 7d) = 4(6 + 7d) = 24 + 28d$$, and hence the sum of the fifth through eighth terms is $$S_8 - S_4 = 12 + 22d$$.

$$12 + 6d = \frac{1}{5}(12 + 22d)$$ 

$$8d = -48 \implies d = -6$$.

Substituting into the formula for the sum of the first twenty terms, we get $$S_{20} = \frac{20}{2}(2 \times 3 + 19(-6)) = 10(6 - 114) = 10(-108) = -1080$$, which is the correct answer Option 1: $$-1080$$.