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
b) -1
c) 2
d) 0

• Let us analyzse the series.
  A(3)=A(2)-A(1)=0
  A(4)=A(3)-A(2)=-1
  A(5)=A(4)-A(3)=-1
  A(6)=A(5)-A(4)=0
  A(7)=A(6)-A(5)=1
  A(8)=A(8)-A(6)=1
  So, The series is repeating after every six term.
  Also , Sum of all numbers from 1 to 6 is 0.
  i.e S(6)=0.
  Similarly , S(12),S(18),S(24), all are zero.
  So,the sum is zero when number is divisible by 6.
  
  Now, We have n=1000
  Now,1000 mod 6 =4.
  So S(1000)=S(4).
  
  S(1000)=S(4)=S(1)+S(2)+S(3)+S(4)
  =>S(1000)=1+1+0+(-1)
  Therefore, S(1000) = 1.
  
• 8 years agoHelpfull: Yes(29) No(0)
• 0 is the answer.
• 8 years agoHelpfull: Yes(10) No(5)
• The Sequence repeats after 6 terms (i.e 1,1,0,-1,-1,0...so on) So if we calculate 1000 mod 6 we get 4 as the remainder.
  S(1000) = S(4) = A(1)+A(2)+A(3)+A(4) = 1 + 1 + 0 - 1 = 1
• 8 years agoHelpfull: Yes(7) No(0)
• 1
  bcoz value of A(1)=1 is repeating after every 6th term i.e. A(7)=1 therefore S(6)=0
  hence if we divide 1000 by 6 then reminder will be 4 n hence S(996)=0
  n sum remaining 4 terms is 1(1+1+0+(-1)=1) S(1000)=1
• 8 years agoHelpfull: Yes(1) No(0)
• Sequence Follows
  1,1,0,-1,-1,0,1,1,0,-1,-1,..........
  Sum of First 5 terms is 0
  Answer is 0
  Option (d)
• 8 years agoHelpfull: Yes(0) No(4)
• 1 is the answer.
  s(1000)=A(1)+A(2)+A(3)+.....A(1000).
  Leave A(1), A(2) behind since values known.
  A(3) =A(2)-A(1)
  A(4)=A(3)-A(2)
  A(5)=A(4)-A(3)
  ..........................
  A(1000) = A(999)-A(998)
  .....
  As you can see each term first after equaltity gets cancelled with second term in the next equality. Hence all except A(999) and A(1) remains
  which implies : s(1000) = A(1)+ A(2) + A(999) - A(1)
  = A(999) + 1
  Now, A(999) = A(998) -A(997)
  =A(997)-A(996)-A(997)
  =-A(996)
  Similary for every three difference this cycle repeats which means it occurs 329 times. After which it will be A(3) which is 0
  s(1000)=0+1=1
• 8 years agoHelpfull: Yes(0) No(0)
• 0 ans ascalcultd
• 8 years agoHelpfull: Yes(0) No(2)
• given A(1)=A(2)=1
  A(3)=A(2)-A(1)=1-1=0
  A(4)=A(3)-A(2)=0-1=-1
  A(5)=A(4)-A(3)=-1-0=-1
  A(6)=A(5)-A(4)=-1-(-1)=0
  !
  .
  .
  .
  Series coming is 1,1,0,-1,-1,0,1,1,0.........see adding we get zero only so, answer is zero(0).
• 8 years agoHelpfull: Yes(0) No(3)