Geometric series, find the common ratio.

Jul 2015
559
14
United States
Given: a=1, 7th term = 4096.


formula that we have to use: a_n=ar^n-1



if we plug it in we get: 1=ar^0
4096=ar^6
If we divide the 2nd equation by the first equation all we get is 4096=r^6..... now the answer is +-4....... so am I suppose to know off the top of my head that 4096 is 4^6..... so then... 4^6=r^6...... square root both sides by 6........ r=+-4......


There must be a simpler way to do this.
 
Jul 2015
559
14
United States
I was right... so r^6=4096...... square both sides by 6.... r=+-4...
 

Debsta

MHF Helper
Oct 2009
1,279
583
Brisbane
If you don't know it off the top of your head, you could use a calculator and find the 6th root of 4096.
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
A geometric series is of the form $x_1= a$, $x_2= ar$, $x_3= ar^2$, $\cdot\cdot\cdot$, $x_n= ar^{n-1}$. So if you know the first term is $x_1= 1$, then the 7th term is $r^{7-1}= r^6= 4096$. To find r, find the 6th root of 4096. That is, as you might expect, a small integer.