My Math Forum Arithmetic Progression help!

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 March 22nd, 2011, 06:28 AM #1 Member   Joined: Nov 2010 Posts: 39 Thanks: 0 Arithmetic Progression help! for hours i've been dealing with this problem and yet i cant really solve it. can you please help me with this one. PROBLEM The fifth term of an arithmetic sequence is 24 and the sum of the first 10 terms is 265. write the first three terms of the sequence. please help me. thank you in advance.
 March 22nd, 2011, 07:02 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Arithmetic Progression help! (1): sum of an arithmetic series: $S_n\,=\,\frac{n}{2}$2a_1\,+\,(n\,-\,1)d$$ (2): nth term of an arithmetic progression: $a_n\,=\,a_1\,+\,(n\,-\,1)d$ From (1): $265\,=\,5$2a_1\,+\,9d$\,=\,10a_1\,+\,45d$ (3) From (2): $24\,=\,a_1\,+\,4d$ (4) Multiply (4) by 10: $240\,=\,10a_1\,+\,40d$ (5) Subtract (5) from (3): $25\,=\,5d,\,d\,=\,5$ First 3 terms: 4, 9, 14 . . .

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