Difficult Math Problem #120 - Sequences

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 354
Joined: Tue Jun 27, 2006 9:20 pm
Thanked: 11 times
Followed by:5 members

Difficult Math Problem #120 - Sequences

by 800guy » Wed Apr 18, 2007 8:18 am
Sequence A and B. a1=1, b1=k. an=b(n-1)-a(n-1) bn=b(n-1)+a(n-1). What is a4=?

from difficult math problems doc, oa coming after people answer with questions

User avatar
Community Manager
Posts: 789
Joined: Sun Jan 28, 2007 3:51 pm
Location: Silicon valley, California
Thanked: 30 times
Followed by:1 members
800guy wrote:Sequence A and B. a1=1, b1=k. an=b(n-1)-a(n-1) bn=b(n-1)+a(n-1). What is a4=?

from difficult math problems doc, oa coming after people answer with questions
a4 = b3 - a3
= (b2 + a2) - (b2 - a2)
= 2a2
= 2 (b1 - a1)
= 2(k - 1)

Legendary Member
Posts: 559
Joined: Tue Mar 27, 2007 1:29 am
Thanked: 5 times
Followed by:2 members

by Cybermusings » Thu Apr 19, 2007 2:13 am
a4 = a(4-1)+b(4-1)
=a3+b3
Now a3=a(3-1)-b(3-1)
and b3=a(3-1)+b(3-1)
a3+b3 =a2-b2+a2+b2
=2a2
a2=a(2-1)-b(2-1)
=a1-b1
=1-k
so 2a2=2(1-k)

Master | Next Rank: 500 Posts
Posts: 354
Joined: Tue Jun 27, 2006 9:20 pm
Thanked: 11 times
Followed by:5 members

OA

by 800guy » Fri Apr 20, 2007 8:43 am
OA:

a2 = k-1 ; b2 = k+1

a3= (k+1)-(k-1) = 2 ; b3 = (k+1)+(k-1) = 2k

a4 = 2k - 2 = 2(k-1) = 2(b1-a1)

Junior | Next Rank: 30 Posts
Posts: 26
Joined: Mon Apr 09, 2007 6:20 am
Thanked: 2 times

by rajeshvellanki » Sat Apr 21, 2007 8:27 am
long mehtod:

a1=1;b1=k

a2=b1-a1
==> a2=k-1

b2=b1+a1
==>b2=k+1

a3=b2-a2
a3=(k+1)-(k-1)
==>a3=2

b3=b2+a2
b3=(k+1)+(k-1)
==>b=2k

k now

a4=b3-a3
a4=(2k)-(2)
==>a4=2(k-1)


so ----------------a4=2(k-1)--------------------