What is the formula for finding the common ratio in a geometric sequence?

[temaire]

Homework Statement

On an exam question, although I can not remember the details, it gave us a table that looks similar to the table below.

http://img403.imageshack.us/img403/9703/geoseqpr4.png​

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The question tells us that the graph is a geometric sequence, and says to use a formula to determine what the common ratio is.

Homework Equations

$$t_n=ar^n^-^1$$
$$A=P(1+i)^n$$

The Attempt at a Solution

Although the question did not specify which formula to use, I used the second one that I listed above. Would this be acceptable to determine the common ratio, or was the question expecting us to use the general term formula?

 

[dirk_mec1]

Both formulas can be used. (why?)

 

[HallsofIvy]

Those are both the same with A= t_n, r= 1+ i, and a= P(1+i).

However, the second equation is NOT normally given as a 'geometric sequence' formula. It is the formula for the amount in, say, a bank account, when the initial amount put into the account was P and the account compounded annually, for n years, at interest i.

You should be able to get the correct answer using either one. did the problem really say to "use a formula"? Learning mathematics is more about learning definitions than formulas. I would simply say that the common ratio is simply the ratio of the population at one year to the population the previous year- if this is a geometric sequence then all such ratios should be the same: 20/10= 40/20= 2. The "common ratio" is 2.

 

[temaire]

Both formulas can be used. (why?)

Actually, I think the question more specifically asked to use a geometric sequence formula, and I used the second one that I listed. Now, I'm wondering if I will lose marks for not using the general term formula, because it is known as the geometric sequence formula. The reason why I used the second formula on the exam is because I thought it was just another form of the general term formula, and that it would be acceptable.

 

[temaire]

did the problem really say to "use a formula"?

Like I said at first, I don't quite remember the exact details of the question, but you had to find the common ratio (although they don't tell you directly) and put it into a percentage. Also, if you read my post above, you will see that I corrected myself.