In a sequence of integers, A(n) = A(n-1) - A(n-2), where A(n) is the n th term in the sequence, n
is an integer and n >=3, A(1)=1,A(2)=1 . Calculate S(1000), where S(1000) is the sum of the first
1000 terms

• A(1)=1
  A(2)=1
  A(3)=1-1=0
  A(4)=0-1=-1
  A(5)=-1-0=-1
  A(6)=-1-(-1)=0
  A(7)=0-(-1)=1
  A(8)=1-0=1
  And so on.... we can clearly see that After every n/6 sum of n no become 0
  
  So till S(996) total will be 0
  A(997)=1
  A(998)=1
  A(999)=0
  A(1000)=-1
  So S(1000) = 1
  so 1 is the answer.
• 9 years agoHelpfull: Yes(15) No(1)
• answer =1.
  see a(1)=1;
  a(2)=1;
  a(3)=a(2)-a(1)=1-1=0;
  a(4)=-1;
  a(5)=-1;
  a(6)=-2;
  a(7)=-1;
  a(8)=1;
  a(9)=2;
  a(10)=1;
  so the sum of first 10 is 1;
  some will be same for every 10 terms;
  so the ans. will be 1.
• 9 years agoHelpfull: Yes(1) No(0)
• 500500
  =n(n+1)/2
  =1000(1001)/2
  =500500
• 9 years agoHelpfull: Yes(0) No(8)