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 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, $\displaystyle S_n = \frac{b_1 (q^n -1)}{q-1}$ to find n, then find x, $\displaystyle b_n=b_1 q^{n-1}$ March 28th, 2015, 02:31 AM   #3
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 Originally Posted by tahirimanov19 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, $\displaystyle S_n = \frac{b_1 (q^n -1)}{q-1}$ to find n, then find x, $\displaystyle b_n=b_1 q^{n-1}$

I'm having problem with dragging out n from Sum Formula $\displaystyle S_n = \frac{b_1 (q^n -1)}{q-1}$ ,can you or someone else please show/explain how to drag out n= please ? March 28th, 2015, 02:54 AM   #4
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 Originally Posted by atest0504 Thanks for reply I'm having problem with dragging out n from Sum Formula $\displaystyle S_n = \frac{b_1 (q^n -1)}{q-1}$ ,can you or someone else please show/explain how to drag out n= please ?
$\displaystyle 26214 = \frac{-2 \times ((-4)^n -1)}{-5}$

$\displaystyle 65536=(-4)^n \Rightarrow n=8$ March 28th, 2015, 03:25 AM   #5
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 Originally Posted by tahirimanov19 $\displaystyle 26214 = \frac{-2 \times ((-4)^n -1)}{-5}$ $\displaystyle 65536=(-4)^n \Rightarrow n=8$
How did you get from 26214 to 65536 (2 to the 16th power) ?
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) $\displaystyle n = 8$ Thanks from atest0504 March 28th, 2015, 06:12 AM #7 Newbie   Joined: Mar 2015 From: Slovenia Posts: 6 Thanks: 0 Is the final result $\displaystyle X=-2 (-4)^{8-1} = 32768$ ? March 28th, 2015, 09:57 AM   #8
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 Originally Posted by atest0504 Is the final result $\displaystyle X=-2 (-4)^{8-1} = 32768$ ?
Can someone please confirm if I calculated it right asap and if I failed please give me correct result.I'm in kind of hurry.
Thanks.. March 28th, 2015, 11:17 AM   #9
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 Originally Posted by atest0504 Is the final result $\displaystyle X=-2 (-4)^{8-1} = 32768$ ?

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 $\displaystyle a=-2$ $\displaystyle r=\frac{8}{-2}=-4$ $\displaystyle S_n=\frac{a(r^n-1)}{r-1}$ $\displaystyle 26214=\frac{-2(-4^n-1)}{-4-1}$ $\displaystyle -131070=-2(-4^n-1)$ $\displaystyle 65535=-4^n-1$ $\displaystyle (-4)^n=65536$ $\displaystyle (-4)^n=4^8$ $\displaystyle n=8$ $\displaystyle T_n=ar^{n-1}$ $\displaystyle T_8=ar^7$ $\displaystyle =-2(-4)^7$ $\displaystyle =32768$ Thanks from atest0504 Last edited by jiasyuen; March 28th, 2015 at 04:34 PM. Tags geometric, progression Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jiasyuen Algebra 1 May 14th, 2014 08:19 AM jiasyuen Algebra 1 May 1st, 2014 03:40 AM Ter Algebra 2 April 13th, 2012 05:34 AM islam Number Theory 3 July 20th, 2011 06:39 AM MIDI Elementary Math 10 January 23rd, 2011 05:09 AM

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