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October 15th, 2011, 07:57 AM   #1
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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
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October 15th, 2011, 09:40 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...

, where

is the nth term,

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

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

When we plug in the known values, this formula simplifies to . This is, effectively, the summand in the series.

But the formula for a finite series is



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