Let a, b and c be the 7^th, 11^th and 13^th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then $${a \over c}$$ equal to :

If a, b, c be three distinct real numbers in G.P. and a + b + c = xb , then x cannot be

Let $${a_1},{a_2},.......,{a_{30}}$$ be an A.P.,

$$S = \sum\limits_{i = 1}^{30} {{a_i}} $$ and $$T = \sum\limits_{i = 1}^{15} {{a_{\left( {2i - 1} \right)}}} $$.

If $$a_5$$ = 27 and S - 2T = 75, then $$a_{10}$$ is equal to :

The sum of the first 20 terms of the series

$$1 + {3 \over 2} + {7 \over 4} + {{15} \over 8} + {{31} \over {16}} + ...,$$ is :