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March 7th, 2010, 11:29 AM  #1 
Newbie Joined: Mar 2010 Posts: 1 Thanks: 0  don't get it :(
Hi all, i'm new here so if i don't do this right soooorry the question is about arithmetic series and i get them but i haven't come across a question like this before and i don't get what to do... it says the first term of an arithmetic series is 3 and the seventh term is twice the third term. (i) find the common difference ( i know for the common difference you need to have a constant addition or subtraction rule but i don't get how to work it out :S) (ii) calculate the sm of the first 20 terms of the series (i know the equation but i don't know how to use it :S ) thank you sooo much and sorry if you've seen questions like these a million times xx 
March 7th, 2010, 02:07 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
Various books use the variable "a" for the first term of an arithmetic progression, and "d" for the common difference, so I'll do the same. Clearly, the nth term is a + (n  1)d, and so the third term is a + 2d and the seventh . . . surely you see where this is heading. (i) You're told that a = 3 and can easily work out that d = 3/2. (ii) Hence the 20th term is . . . ? When you've worked it out, add the first term (i.e., 3) to it and then divided by 2 to find the average of the first twenty terms. Multiplying that by 20 gives you the sum of those terms. This method corresponds to using one of the standard summation formulas that you should have learnt already. 