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

• 9902..
  
  a2= a1+2
  a3= a2+4 == a1+2+4
  a4= a1+2+4+6
  ....
  
  a100= a1+2+4+.. +198
  = a1+ 99/2 * (2+198)
  =9902
• 12 years agoHelpfull: Yes(23) No(4)
• given A(n+1)=A(n)+2n
  A(100)=A(99)+2(99)
  =A(98)+2(98)+2(99)
  =A(97)+2(97)+2(98)+2(99) and so on...
  
  =A(1)+2(1)+..........+2(98)+2(99)
  =2+2(1)+2(2)+.......+2(98)+2(99)
  =2+2(1+2+3+........+98+99)
  =2+2(99*100)/2 since sum of n natural no's=n*(n+1)/2
  =9902 is answer
• 12 years agoHelpfull: Yes(13) No(2)
• please write correct questions
  
• 12 years agoHelpfull: Yes(1) No(5)