1. ## Geometric Progression

Hi

The first three terms of a geometric progression are $\displaystyle 2^n$, 2^(n+1),2^(n+2).

(a) Find n.

(b) Find the sum of the first 6 terms. Express your answer as a rational number.

Could someone please show me how to do (a)? I only know the basics of geometric progression (i.e. the formulas) but none of them fit this question somehow.

2. Originally Posted by xwrathbringerx
Hi

The first three terms of a geometric progression are $\displaystyle 2^n$, 2^(n+1),2^(n+2).

(a) Find n.

(b) Find the sum of the first 6 terms. Express your answer as a rational number.

Could someone please show me how to do (a)? I only know the basics of geometric progression (i.e. the formulas) but none of them fit this question somehow.
I would hazard a guess that as it stands (a) makes no sense. Try posting the question as it is asked.

.

3. typed it word for word from the textbook

By the way, the answers given by the textbook are:

(a) n = 1/2

(b) 93 622.5

4. ## Re :

It is not possible .

$\displaystyle \frac{2^{n+1}}{2^n}=\frac{2^{n+2}}{2^{n+1}}$ , which simplifies to

2=2

$\displaystyle \frac{2^{n+1}}{2^n}=\frac{2^{n+2}}{2^{n+1}}$ , which simplifies to
Which is OK as we have a geometric progression with first term $\displaystyle 2^n$ and common ratio of $\displaystyle 2$. As it stands there is no way to say anything about $\displaystyle n$