# Question #bfd15

Jun 17, 2017

$n = 12$

#### Explanation:

The geometric sequence is ${2}^{1} , {2}^{2} , {2}^{3} \ldots \ldots . . , {2}^{n}$

Here the first term and common ratio are $a = 2 \mathmr{and} r = 2$

We know sum ${s}_{n} = a \cdot \frac{{r}^{n} - 1}{r - 1} \therefore 2 \cdot \frac{{2}^{n} - 1}{2 - 1} = 8190$ or

${2}^{n} - 1 = \frac{8190}{2} = 4095 \mathmr{and} {2}^{n} = 4096 \mathmr{and} {2}^{n} = {2}^{12} \therefore n = 12$ [Ans]