Genral Term

**Curious_eager** · August 18th 2009, 08:48 AM

Hi,

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

Thanks!!!

**Wilmer** · August 18th 2009, 09:00 AM

Geometric Series

Btw, what does "genral" mean?

**bandedkrait** · August 19th 2009, 11:03 PM

The general term of any geometric sequence is given by

Tn = $ar^{n-1}$

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

So we have here,

T3=1
T7=8

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

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

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

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

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

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