March 28th, 2015, 01:58 AM  #1 
Newbie Joined: Mar 2015 From: Slovenia Posts: 6 Thanks: 0  Geometric progression
Hello I've got a problem with solving this geometric progression example: 2 +8 32+ ..... +x =26214 < We are looking for value of x I'm writing a math essay on Monday and I need to learn this example. So, I'd like to ask for some help. Thanks in advance. Last edited by skipjack; March 28th, 2015 at 08:19 PM. 
March 28th, 2015, 02:17 AM  #2 
Newbie Joined: Mar 2015 From: Planet Earth Posts: 13 Thanks: 1 
You have all the neccessary information. ($\displaystyle b_1=2, \; \; q=4, \; \; S_n = 26214$ and you need to find $\displaystyle b_n$). Use Sum formula for geometric progression, $\displaystyle S_n = \frac{b_1 (q^n 1)}{q1}$ to find n, then find x, $\displaystyle b_n=b_1 q^{n1}$ 
March 28th, 2015, 02:31 AM  #3  
Newbie Joined: Mar 2015 From: Slovenia Posts: 6 Thanks: 0  Quote:
I'm having problem with dragging out n from Sum Formula $\displaystyle S_n = \frac{b_1 (q^n 1)}{q1}$ ,can you or someone else please show/explain how to drag out n= please ?  
March 28th, 2015, 02:54 AM  #4  
Newbie Joined: Mar 2015 From: Planet Earth Posts: 13 Thanks: 1  Quote:
$\displaystyle 65536=(4)^n \Rightarrow n=8$  
March 28th, 2015, 03:25 AM  #5  
Newbie Joined: Mar 2015 From: Slovenia Posts: 6 Thanks: 0  Quote:
Where did go 2 1 and 5 from this formula: $\displaystyle 26214 = \frac{2 \times ((4)^n 1)}{5}$  
March 28th, 2015, 05:38 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
$\displaystyle 26214 = \frac{2 \times ((4)^n 1)}{5}$ $\displaystyle 26214 \times 5/2 = \frac{1 \times ((4)^n 1)}{1} = (4)^n  1$ $\displaystyle 131070/2 + 1 = (4)^n$ $\displaystyle 65535 + 1 = (4)^n$ $\displaystyle 65536 = (4)^n$ $\displaystyle 4^8 = (4)^n = 4^n\ $ (if $n$ is even) $\displaystyle n = 8$ 
March 28th, 2015, 06:12 AM  #7 
Newbie Joined: Mar 2015 From: Slovenia Posts: 6 Thanks: 0 
Is the final result $\displaystyle X=2 (4)^{81} = 32768$ ?

March 28th, 2015, 09:57 AM  #8 
Newbie Joined: Mar 2015 From: Slovenia Posts: 6 Thanks: 0  
March 28th, 2015, 11:17 AM  #9 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  x = 32,768 is the answer.$\displaystyle \ \ \ \ \ \ \ $Keep it lower case x. By the way, 2 + 8  32 + ... + x is a geometric series. And 2, 8, 32, ... , x is the corresponding geometric progression. 
March 28th, 2015, 04:29 PM  #10 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
$\displaystyle a=2$ $\displaystyle r=\frac{8}{2}=4$ $\displaystyle S_n=\frac{a(r^n1)}{r1}$ $\displaystyle 26214=\frac{2(4^n1)}{41}$ $\displaystyle 131070=2(4^n1)$ $\displaystyle 65535=4^n1$ $\displaystyle (4)^n=65536$ $\displaystyle (4)^n=4^8$ $\displaystyle n=8$ $\displaystyle T_n=ar^{n1}$ $\displaystyle T_8=ar^7$ $\displaystyle =2(4)^7$ $\displaystyle =32768$ Last edited by jiasyuen; March 28th, 2015 at 04:34 PM. 

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