Algebra Pre-Algebra and Basic Algebra Math Forum

 April 7th, 2014, 12:52 AM #1 Newbie   Joined: Mar 2014 From: Australia Posts: 3 Thanks: 0 Geometric Series Hi everyone, And thank you for the assistance last time asked for help. I have a question posed to me by my tutor. Unfortunately, the tutor is away for 2 weeks so I have no one to ask for direction. The question is "For the Geometric progression with T3 = 3 and T10 = 6561, determine the first term, common ratio, and the sum of the first 20 terms." I am using the following formula........... an = a1 + (n - 1)d 3 = a1 + (3 - 1)d 6561 = a1 + (10 - 1)d a1 = 3 - (3 - 1)d a1 = 6561 - (10 - 1)d 3 - (3 - 1)d = 6561 - (10 - 1)d 6561 - 3 = (10 - 1)d - (3 - 1)d 6558 = 10d - d - 3d + d 6558 = 7d d = 6558/7 d = 936.86 For T3 = 3 3 = a1 + (3 - 1)936.86 3 = a1 + 2 x 936.86 a1 = 3 - 1873.72 a1 = -1870.72 I am not asking for answers......... just want to know if I am on solid foundations. Thanks Phil April 7th, 2014, 04:03 AM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,974 Thanks: 1156 Math Focus: Elementary mathematics and beyond You say you are working with a geometric series but you are using the formula for an arithmetic series! nth term of a geometric series (with a as the first term and r as the common ratio): $a\cdot r^{n-1}$ So we have $a\cdot r^2=3$ and $a\cdot r^9=6561$. Solve for a in terms of r in the first and substitute that into the second to find r. Now use the formula for the sum of a geometric series with $n=20$: $$S=\frac{a(1-r^n)}{1-r}$$ Last edited by greg1313; April 7th, 2014 at 04:16 AM. Tags geometric, series 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 najaa Algebra 4 February 1st, 2012 09:25 AM xela95 Algebra 5 June 17th, 2011 03:17 PM The Chaz Real Analysis 11 February 7th, 2011 05:52 AM cindyyo Algebra 2 August 24th, 2008 02:25 AM clooneyisagenius Real Analysis 1 January 30th, 2008 01:50 AM

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