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 May 3rd, 2016, 10:37 PM #1 Member   Joined: Aug 2014 From: Lithuania Posts: 60 Thanks: 3 Arithmetic progression A finite arithmetic progression is given such that $\displaystyle S_n>0$ and $\displaystyle d>0$. If the first member of the progression remains the same but $\displaystyle d$ increases 2 times, then $\displaystyle S_n$ increases 3 times. If the first member of the progression remains the same but $\displaystyle d$ increases 4 times, then $\displaystyle S_n$ increases 5 times. Find $\displaystyle d$. My try: $\displaystyle S_n=\frac{2a_1+d(n-1)}{2}\cdot n$ $\displaystyle \frac{2a_1+2d(n-1)}{2}\cdot n=S_n=\frac{2a_1+d(n-1)}{2}\cdot n \cdot 3$ $\displaystyle \frac{2a_1+4d(n-1)}{2}\cdot n=S_n=\frac{2a_1+d(n-1)}{2}\cdot n \cdot 5$ When I try to solve this I get $\displaystyle a_1=0$ which is clearly not possible. Can somebody explain me what am I doing wrong? May 4th, 2016, 03:51 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,747 Thanks: 2133 There is no solution. Was the problem originally in English? If not, what was the original wording in full? May 4th, 2016, 07:33 AM #3 Member   Joined: Aug 2014 From: Lithuania Posts: 60 Thanks: 3 I am sorry. I made a mistake in the problem statement. The first part of the problem is: "If the first member of the progression remains the same but $\displaystyle d$ increases by 2, then $\displaystyle S_n$ increases 3 times." Everything else is the same. I solved the equations and got $\displaystyle d=\frac{4}{3}$. Again, I am deeply sorry for the confusion. May 14th, 2016, 10:06 AM #4 Newbie   Joined: May 2016 From: India Posts: 2 Thanks: 1 You may find hints regarding Arithmetic Progression on Welcome to prep4paper.com Tags arithmetic, 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 1st, 2014 03:40 AM will.i.am1 Algebra 14 May 29th, 2013 06:27 AM will.i.am1 Algebra 1 May 27th, 2013 02:23 PM Daksh Algebra 3 November 22nd, 2012 09:08 PM panky Algebra 4 November 17th, 2011 07:05 AM

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