Home » Ask & Discuss » Mathematics. » Algebra « Back to Discussion

Algebra

New kid on the Block

Joined:	24 Nov 2009
Post:	13

3 Dec 2009 05:11:29 IST

0 People liked this

775

can anyone give me the formula of the series... 1,1,5,17,61,217...

None

can anyone give me the formula of the series...1,1,5,17,61,217...

Share this article on:

Comments (4)

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

3 Dec 2009 05:53:09 IST

Like 7 people liked this

5 = 3 x 1 + 2 x 1

17 = 3 x 5 + 2 x 1

61 = 3 x 17 + 2 x 5

217 = 3 x 61 + 2 x 17

so general term is given by : t_n = 3t_n-1 + 2t_n-2

The wicked warrior ''Anurag the devil''

Blazing goIITian

Joined: 28 Oct 2009

Posts: 594

3 Dec 2009 06:32:13 IST

Like 0 people liked this

what will be the sum of this series

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

3 Dec 2009 07:32:24 IST

Like 7 people liked this

analytical expression for n^th term can be found by generating polynomial which I learned from Hari sir.

We have to find : such that

Adding these three :

except 1st terms all terms are 0 since they follow a_n+2 = 3a_n+1 + 2a_n

we know a₁ = 1 and a₂ = 1. Expand RHS and compare coefficients of xⁿ to find out the analytical expression for a_n ( feeling a bit lazy so didn't do till last step :D )

however I can't figure out what will be the sum of the series

edison

Forum Expert

Joined: 19 Oct 2006

Posts: 7537

3 Dec 2009 08:44:06 IST

Like 0 people liked this

Very good one Bipin

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team