# Geometric progressions, i seem to be messing up on simple algebra

• mr_coffee
In summary, the conversation is about solving a geometric progression using a calculator. The problem involves finding the term after the last term and multiplying it by the ratio. After attempting the solution, the person is confused and looking for help. The final simplified solution is 4*3^(n-2).
mr_coffee
hello everyone, I'm trying to figure out this geometric progession and I'm checking it with my calculator and I'm definatley not getting what they are getting:

I'm trying to find the term after the last term, I found the ratio which is 3/2, now I must multiply that ratio by the last term which is:
(2^3)*3^(n-3)
So i'd have:
(3/2)*(2^3)*3^(n-3)
The calculator spits out:
(4/9)*3^n

I did this problem before and I got that I don't know where my brain is, but now I'm getting:

4*3^(n-2);

Becuase the 2 will cancel out the 8, and leave you 4, and 3 x 3^(n-3) is like 3^(n-3+1) = 3^(n-2)

What am I missing?

Here is the geometric progression and below is my work, once I apply the formula its simple aglebra and adding of exponents but I keep screwing it up.
http://suprfile.com/src/1/4ds5zep/lastscan.jpg

Thanks!

Last edited by a moderator:
$$4\times 3^{n-2} = \frac{4}{3^{2-n}} = (\frac{2}{3})^{2}\times 3^{n} = \frac{4}{9}\times \;3^{n}$$

Last edited:

## 1. What is a geometric progression?

A geometric progression is a sequence of numbers where each term is obtained by multiplying the previous term by a constant value. For example, the sequence 1, 2, 4, 8, 16 is a geometric progression with a common ratio of 2.

## 2. How do I find the common ratio in a geometric progression?

The common ratio can be found by dividing any term in the sequence by the previous term. This will give you the same value for all ratios in the sequence.

## 3. What is the formula for finding the nth term in a geometric progression?

The formula for finding the nth term in a geometric progression is an = a1 * rn-1, where an is the nth term, a1 is the first term, and r is the common ratio.

## 4. How do I find the sum of a finite geometric progression?

The formula for finding the sum of a finite geometric progression is Sn = a1 (1 - rn) / (1 - r), where Sn is the sum, a1 is the first term, r is the common ratio, and n is the number of terms in the sequence.

## 5. What are some real-life applications of geometric progressions?

Geometric progressions are commonly used in finance, such as calculating compound interest. They are also used in population growth models, where the population increases or decreases by a constant factor each year. Additionally, geometric progressions can be seen in music, where an octave is divided into 12 equal intervals, each with a frequency ratio of 2:1.

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