Find the sum or a Geometric series 1, 3, 9, 27, 81 ......... for N terms.
I. $$N^{th}$$ term is 729.
II. Next term after the $$N^{th}$$ term is thrice of it.

Sum of $$'n'$$ terms of G.P. = $$\frac{a(r^n-1)}{r-1}$$

Now, using the first statement, if we know the $$n^{th}$$ term, then we can find the value of $$n$$ and hence the sum of $$n$$ terms.

Now, the second statement states that the next term after the $$N^{th}$$ term is thrice of it, which only means that the common ratio $$r=3$$, and thus we cannot find the sum using this statement.

Hence, the question can be answered using only one statement alone.

=> Ans - (A)