Geometric Sequence Help

**fletch** · July 13th 2010, 01:46 PM

Having trouble finding a way of working through this problem:

A geometric sequence has first term 1. The ninth term exceeds the fifth term by 240. Find possible values for the eighth term.

I know that the common ratio has to be 2 because the difference between the two terms is small number, but this was found through trial and error.

Any help would be appreciated.

**Plato** · July 13th 2010, 02:14 PM

Originally Posted by fletch

Having trouble finding a way of working through this problem:

A geometric sequence has first term 1. The ninth term exceeds the fifth term by 240. Find possible values for the eighth term.

I know that the common ratio has to be 2 because the difference between the two terms is small number, but this was found through trial and error.

I am not sure what you are asking.
You are given that $a_1=1,~a_5=r^4,~\&~a_9=r^8$ .
Also $a_9-a_5=240$ .
From that find $r$ .

**Archie Meade** · July 13th 2010, 03:46 PM

Originally Posted by fletch

Having trouble finding a way of working through this problem:

A geometric sequence has first term 1. The ninth term exceeds the fifth term by 240. Find possible values for the eighth term.

I know that the common ratio has to be 2 because the difference between the two terms is small number, but this was found through trial and error.

Any help would be appreciated.

The geometric sequence is

$1,\ r,\ r^2,\ r^3,\ r^4,\ r^5,\ r^6,\ r^7,\ r^8,\ r^9....$

From your information

$\left(r^4\right)^2=r^4+240$

$x^2-x-240=0$

$(x-16)(x+15)=0$

x is not -15, so x is 16

r is the 4th root of 16, which is $\pm2$ .

The 5th and 9th terms are both positive, regardless of whether r is 2 or -2

The 8th term is the two solutions to $r^7$

Thread: Geometric Sequence Help

LinkBack

Thread Tools

Display

Geometric Sequence Help

Similar Math Help Forum Discussions

Geometric Sequence

geometric sequence help

Arithmetic sequence, geometric sequence, & geometric series

geometric sequence

set, geometric sequence,fraction and arithmetic sequence

Search Tags