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

• The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n.
  The value of 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
• 12 years agoHelpfull: Yes(78) No(1)
• here is a quicker way......
  quickly find the values of n=2,3,4,5,6
  we get for n=2 4
  n=3 8 ( 1 less than its square i.e.9)
  n=4 14 (2 less than its square i.e 16)
  n=5 22 (3 less than its square i.e 25)
  continuing ... for n=100 it will be 98 less than its square
  so (100^2)-98=9902 ans
• 12 years agoHelpfull: Yes(34) No(1)
• the answer is 9,902.
  a(100) = (100)(99)+2=9,902
• 12 years agoHelpfull: Yes(6) No(10)
• S1=2+4+8+14+22+.....upto 100terms
  S1= 2+4+8 +14+22+...upto 99terms
  
  subtracting the two series we get,
  2+[2+4+6+8+.....upto 99 terms](an AP series)...
  Solve it...
• 12 years agoHelpfull: Yes(1) No(11)
• let a=2 , d=2,a.p formula find nth term i.e.. tn=a+(n-1)d
  where tn=100...
  100=2+(n-1)2 gives n=50.
  now sum of n terms n/2(a+l)=2550(ans).
• 12 years agoHelpfull: Yes(0) No(30)