My Math Forum Arithmetic Series

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 October 15th, 2011, 08:57 AM #1 Newbie   Joined: Sep 2011 Posts: 16 Thanks: 0 Arithmetic Series Hi, was wondering if anyone could help on these questions please? Would be appreciated!! 1) I have the first 3 terms, they are -3, -1, 1 and the common difference is +2. I need to show that n ? (2r-5) = n(n-4) r=1 2) The first term of an arithmetic sequence is 30 and the common difference is -1.5 It asked me to find the 25th term and I got 300. Then it tells me the rth term of the sequence is 0. * And asks me to find the value of r? Then it tells me the sum of the first n terms of the sequence is Sn. * And asks me to find the largest positive value of Sn? Any help would be great and if possible to show the working out as I have more questions like these. Thanks
October 15th, 2011, 10:40 AM   #2
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Re: Arithmetic Series

Quote:
 Originally Posted by poochie03 Hi, was wondering if anyone could help on these questions please? Would be appreciated!! 1) I have the first 3 terms, they are -3, -1, 1 and the common difference is +2. I need to show that n ? (2r-5) = n(n-4) r=1 ...
Recall the formula for the nth term of an arithmetic progression...

$a_n= a_1 + (n - 1) \cdot d$, where

$a_n$ is the nth term,

$a_1$ is the first term ( = -3 in this example), and

$d$ is the difference ( = 2, as you have found)

When we plug in the known values, this formula simplifies to $a_n= 2n -5$. This is, effectively, the summand in the series.

But the formula for a finite series is

$S_n= \frac{n}{2} \cdot (a_1 + a_n)$

Substitute the known values into this formula and it will match exactly (after simplifying).

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# rth term of a sequence is 0

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