# Thread: Genral Term

1. ## Genral Term

Hi,

Find the genral term of the G.P with third term 1 and the seventh term 8?

Thanks!!!

2. Geometric Series

Btw, what does "genral" mean?

3. The general term of any geometric sequence is given by

Tn = $\displaystyle ar^{n-1}$

where clearly, $\displaystyle a$ is the first term and $\displaystyle r$ is the common ratio of the geometric progression.

So we have here,

T3=1
T7=8

i.e. $\displaystyle ar^2=1$............(1)
and$\displaystyle ar^6=8$............(2)

Divide (2) by (1) to eliminate a
so we have, $\displaystyle {r^6}/{r^2}$= 8/1

so $\displaystyle r^4=8$
$\displaystyle i.e. r = 8^{1/4}$

$\displaystyle Now using the fact that ar^2=1$
$\displaystyle we have, a(8)^{1/2}=1$

$\displaystyle so a = 8^{-1/2}$

$\displaystyle Hence the general term of the series is given by$
$\displaystyle Tn= 8^{-1/2}(8^{1/4})^{n-1}$

4. Mr Banded Krait, I would like to see a space between your words

5. Originally Posted by Wilmer
Mr Banded Krait, I would like to see a space between your words
$$\text{Hence the general term of the series is given by}$$ gives $\displaystyle \text{Hence the general term of the series is given by}$