sequence and series

Posts 6 · Viewed 6410 · Go to Last Post

· Snapshot

Like · Likedby · 0

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 subscripts].

anugaman

· Snapshot

Like · Liked by · 0

anybody?

NightElf

· Snapshot

Like · Liked by · 0

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

anugaman

· Snapshot

Like · Liked by · 0

i dunt know how to start. formula only doesnt help.anybody

cowboy

· Snapshot

Like · Liked by · 0

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 script using either iteration or recursion. It would be similar to solving a Fibonacci Series.

-Cowboy

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

cowboy

· Snapshot

Like · Liked by · 0

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.

Please log in to reply to this post

You can also log in using your Facebook