just a question. when finding the nth term of a geometric sequence as a function of x , is it possible to have multiple answers nth term functions that are valid?

Question

anonymous · Answer

sorry correction.. * as a function of n...

anonymous · Answer

Formula to find nth term is:

$$\huge t_n = a.r^{n-1}$$

anonymous · Answer

Since n can take only one value at a time so you will have only one particular value...

anonymous · Answer

yes agreed but for a particular geometric sequence, can Tn vary is what im asking

anonymous · Answer

Tn is the last term..
It depends on how we choose the last term..
We will get the last term by putting different values of n..

anonymous · Answer

okay i dont think your understanding me... let me give you an example... the geometric sequence  as such. : 6, -9, 27/2, -81/4, 243/8....... i found that the nth term could possibly be $$A_n= 6(-3/2)^{n-1}$$ but the nth term could also possibly be :$$A _{n}=-4(-3/2)^{n}$$
what im asking is if this is possible to have two different types of equations for the nth term or is one of them incorrect?

anonymous · Answer

How you got the second one?

anonymous · Answer

But their answer will be same..

anonymous · Answer

You did nothing but you solve the equation further..

anonymous · Answer

well i actually didnt get the second one.... this question comes from my textbook... i came up with the first one but the answer in my textbook is the second one.... i tested the 1st 1.. (the one i made) and it works but so does the one from the text book so is it possible for both to be correct or is the one i came up with incorrect?

anonymous · Answer

See,
$$\huge t_n = a.r^{n-1}$$

$$\huge t_n = \frac{a.}{r}r^n$$

anonymous · Answer

See, both the equations are same.

You can write 4 as: 4*1 or you can write it as 2*2

Just the same thing..

anonymous · Answer

but is the first one correct then?

anonymous · Answer

Yes dear first one is the actual formula and the second one is derived from first by just solving it..

anonymous · Answer

okay so they are both in simplified form?

anonymous · Answer

See first one is a standard formula and the second one is just derived from that formula..

anonymous · Answer

Both are the one and the same thing...

anonymous · Answer

okay thank you:)