. The sequence {An} is defined by A1 = 2 and An+1=An+2n what is the value of A100

• A1=2,A2=4,A3=8,A4=14........
  each term is incremented by 2n ie
  1st increment is of 2,then 2nd is 4 then 3rd is of 6 and so on
  so the incement in the terms follows the series 2,4,6,.......198(for 99th term)
  summation of the A.P. series=990
  hence A100 will be incremented by 990 from A1 i.e.
  A100=A1+990=992
• 10 years agoHelpfull: Yes(1) No(1)
• A1=2
  A2=A1+1=A1+2=2+2=4
  A3=A2+1=A2+4=4+4=8
  So the first few terms are 2,4,8,14,22......
  the differences of the above terms are 2,4,6,8,10....
  and the differences of difference are 2,2,2,2 all are equal. So this series represents a quadratic equation
  Assume An=an^2+bn+c
  Now A1=A+b+c=2
  A2=4a+2b+c=4
  A3=9a+3b+c=8
  Solving we get a=1,b=-1,c=2
  Substituting in An:n^2-n+2
  Substitute 100 in above equation we get 9902
  Ans:9902
• 10 years agoHelpfull: Yes(1) No(1)