The sequence {A(n)} is defined by A1 = 2 and A(n+1) = A(n +2n) what is the value of A(100)

• this can also be written as :
  A(n+1)=n^2+n+2
  A(0+1)=0^2+0+2=2
  A(1+1)=1^2+1+2=4
  A(2+1)=2^2+2+2=8
  A(3+1)=3^2+3+2=14
  A(4+1)=4^2+4+2=22
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  A(99+1)=99^2+99+2=9801+99+2=9902
  hence,A(100)=9902
• 11 years agoHelpfull: Yes(14) No(1)
• A1=2
  An+1=An+2n
  A2=A1+2*1=4
  A3=A2+2*2=8
  A4=A3+2*3=14
  A5=A4+2*4=22
  ...A99
  Now solve the above eqns
  A1+A2+A3+A4+...+A99+A100=A1+A2+A3+...+A99+2(1+2+3+4+5+...+99)
  Now eliminate right hand side and left hand side upto A99 then,
  A100=2(1+2+3+4+5+...+99)
  using n integer formula[n*(n+1)/2]
  n=99
  99*(99+1)/2=99*100/2=9900/2=4950
  Thus solution of A100=2*4950=9900
• 11 years agoHelpfull: Yes(7) No(2)
• given A1=2 and An+1=An+2n and A100=?
  lets find out A2=A1+1=A1+2=2+2=4
  SIMILARLY A3=A2+1=A2+2*2=4+4=8
  series is getting followed as 2,4,8...2^n
  hence A100=A99+1=2^99
• 11 years agoHelpfull: Yes(6) No(9)
• given A(1)=2
  A(n+1)=A(n)+2n
  n=1, A(2)=(1*0+2)+2*1=4
  n=2, A(3)=(2*1+2)+2*2=8
  n=3, A(4)=(3*2+2)+2*3=14
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  n=99, A(100)=(99*98+2)+2*99=9902
• 11 years agoHelpfull: Yes(4) No(0)
• A 1 = A 0 = 2
  so A 2 = A 3
  and A 3 = A 6
  A 4 = A 9
  A 5 = A 12
  so A 100 = A 297
  now A 3 - A 2 = A 6 - A 3 ~ A 3
  so A 1 - A 0 = 2 ~A 3
  clearly A 100 = 2*100 = 200 Ans
• 11 years agoHelpfull: Yes(2) No(6)
• But zeba, if u calculate a4 u will get 14 which is not in d series...
• 11 years agoHelpfull: Yes(1) No(1)
• just simple,see
  a_n+1 = a_n + 2n,
  so, a_5 = a_4+2*4 = a_3 +2*3+2*4(since again a_4=a_3 +2*3) = a_2 +2*2+2*3+2*4
  = a_1 + 2(1+2+3+4),
  so from this,
  a_100 = a_1 + 2*(1+2+3+.....+99)= 2+2*(this is sum of n terms) = 2+2*(99*100/2)
  
  = 2+9900 = 9902.
  
• 11 years agoHelpfull: Yes(1) No(0)
• Given- An+1=An+2n.
  So An=An-1 + 2(n-1) and An-1=An-2 + 2(n-2).
  We have An+1=An-2 + 2(n+(n-1)+(n-2)).
  Taking a look at the pattern we can say that similarly -
  An+1= A1 + 2(n+(n-1)+(n-2)......+1).
  An+1=A1 + 2(n)(n+1)/2
  An+1=2 + n(n+1).
  Here n+1=100, n=99,
  So A100= 2 + 99*100 = 9902(ANS)
• 11 years agoHelpfull: Yes(0) No(1)