The sequence {A_n} is defined by A_1= 2 and A_(n+1)=A_n+2n. What is the value of A_100.

• A(1)=2 and A(n+1)=A(n)+2n.
  A(100)=A(99+1)=A(99)+2*99
  =A(98)+2*98+2*99
  =A(97)+2*97+2*98+2*99
  
  ...
  A(100)=A(1)+2*1+2*2+2*3+......+2*98+2*99
  = 2+(2*1+2*2+2*3+......+2*98+2*99)
  = 2+2(1+2+3+.....+98+99)
  = 2+2(sum of the first 99 natural numbers)
  = 2+2(99*100/2) [sum of the first n natural numbers={n*(n+1)/2}]
  = 2+9900
  = 9902
• 11 years agoHelpfull: Yes(39) No(0)
• 9902 is the answer
• 11 years agoHelpfull: Yes(3) No(0)
• A100=2+n(n-1)
  here n is 100
  soo by keeping n=100 we get 9902
• 10 years agoHelpfull: Yes(1) No(0)