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 sequence and series
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Posted on 10-09-09 4:18 AM     Reply [Subscribe]
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Given a series a1, a2.......an. If a1 =-4, a2 =5 and an = a(n-2)-a(n-1), then find the sum of first 100 numbers in the series?
[NOTE: 1, 2, (n- 2), (n-1) and n in the above question are subs].

 
Posted on 10-09-09 3:12 PM     Reply [Subscribe]
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Posted on 10-09-09 3:59 PM     Reply [Subscribe]
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For arithmetic sequence, we have two basic formulas



S = ( n / 2 ) ( A + T )



wherein

S = sum of n terms

n = number of terms

A = first term

T = last term



If the last term is not given instead only the first term is given we use the formula that visibleman_7887 has mentioned



S = ( n / 2 ) [ 2A + ( n - 1 ) * d ]



wherein

S = Sum of n terms

n = number of terms

A = first term

d = common difference

Source:
http://answers.yahoo.com/question/index?qid=20060830202603AASPvcs

 
Posted on 10-09-09 9:57 PM     Reply [Subscribe]
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i dunt know how to start. formula only doesnt help.anybody
 
Posted on 10-09-09 10:19 PM     Reply [Subscribe]
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To give u a hint,  the first 100th sum consists of only two terms N2 and N99 since all the other terms cancel out. There is a very easy method to calculate it. The only terms involved in the final calculation depend upon N1 and N2 only. It's not even necessary to calculate N99.  


If it's not a physics problem but a numerical analysis problem then you can solve it by writing a simple using either iteration or recursion. It would be similar to solving a Fibonacci Series.


-Cowboy

Last edited: 09-Oct-09 10:25 PM

 
Posted on 10-10-09 7:48 PM     Reply [Subscribe]
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Another hint. The final solution is: 2*N2 - N1. I would like you to figure out how it's derived tho.


Regular summation formulas can't be used since the sequence is not monotonous.


 


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