The sequence is defined by A(1)=2 and A(n+1)=A(n)+2n What is the value of A(100)
(1)9902
(2)9900
(3)10100
(4)9904

• 9902
  A(100)=A(99)+2*99
  same here
  A(100)=A(1)+2*(1+2+3+.....+99)
  A(100)=2+9900
  A(100)=9902
  ans is (1)9902
• 12 years agoHelpfull: Yes(12) No(2)
• A(100)= A(99)+2(99)
  A(100)= A(98)+ 2(98)+2(99)
  A(100)= A(97)+2(97)+2(98)+2(99)
  ||LY
  A(100)= A(1)+ 2(1+2+3+4+.......97+98+99)
  
  NOW; 1+2+3.......+97+98+99= 99(2+98)/2= 4950
  (SUM OF AN A.P)
  
  A(100)= 0+ 2(4950)= 9900
• 12 years agoHelpfull: Yes(2) No(13)
• a(1)=2
  a(n+1)= a(n)+2n
  
  a(2)= a(1)+4
  a(3)=a(2)+6
  a(4)= a(3)+8
  .
  .
  .
  a(100) = a(99)+198
  
  adding R.H.S and L.H.S seperatly
  we get
  a(2)+a(3)+a(4)....a(100)= a(1)+a(2)+a(3)....a(99) + (4+6+8+10+....198)
  thus
  a(100)= a(1)+ 9898
  a(100)= 2 +9898
  a(100)= 9900
  ans
• 12 years agoHelpfull: Yes(1) No(5)