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

a. 9900
b. 9902
c. 9910
d. 9916

• given A(n) = 2,A(n+1) = A(n) + 2n
  
  consider A(2) = A(1) + (2)
  
  A(3) = A(2) + 4 => A(3) = A(1) + (2+4)
  
  Similarly
  
  A(4) = A(1) + (2+4+6)
  
  A(100) = A(1) + (2+4+6+.....+198)
  A(100) = 2 + (sum up to 99 terms)
  A(100) = 9902
• 10 years agoHelpfull: Yes(13) No(0)
• We know that A1 = 2 so A1+1=A2=4,A3=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 differences are 2, 2, 2, 2. all are equal. so this series represents a quadratic
  equation.
  Assume An=an2+bn+c
  Now A1 = a + b + c = 2
  A2= 4a + 2b + c = 4
  A3= 9a + 3b + c = 8
  Solving above equations we get a = 1, b = - 1 and C = 2
  So substituting inAn =n2+bn+c =n2-n+2
  Substitute 100 in the above equation we get 9902.
• 10 years agoHelpfull: Yes(7) No(0)
• A(1)=2
  A(2)=A(1)+(1*2)
  A(3)=A(1)+(2*3)
  A(4)=A(1)+(3*4)
  ...............
  A(100)=A(1)+(99*100)=9902
• 10 years agoHelpfull: Yes(5) No(0)
• question is unclear.should be like A(n+1)=A(n)+2n
• 10 years agoHelpfull: Yes(1) No(0)
• 9902
  The series is 2,4,6,8.....99terms. Sum=9900. ans=9900+2=9902
• 10 years agoHelpfull: Yes(0) No(1)
• in q A1=2 &An+1=An+2n
  A2=A1+2
  A3=A2+4=A1+2+4=A1+6
  A4=A1+2+4+6
  SIMILAR
  A100=A1+2+4+6.......198=A1+2(1+2+3......99)
  in ap series
  A1+2((99*100)/2)=A1+9900
  9902
  
• 10 years agoHelpfull: Yes(0) No(0)
• a1=2
  a2=4
  a3=8
  a4=14
  so difference between them are 2 4 6 like this i.e. in ap
  so a100=a1+sum of 99 terms of that ap
  a100=2+9900
  9902
• 10 years agoHelpfull: Yes(0) No(0)