If a1=5. an=an-1 + 2*n then what is the value of a2+a4+....a100?

1) 174400
2) 517800
3) 176400
4) 173400

• a1= 5
  
  a2 =5+2*2 = 9 = 2 ^ 2 + 2 + 3
  
  a3 =9 + 2 * 3 =15 = 3 ^ 2 + 3 + 3
  
  a4 = 15+2*4= 23 = 4 ^ 2 + 4 + 3
  
  a{n} = n ^ 2 + n + 3
  
  Required Sum = (2^2+4^2+6² +......+ 100 ²) + ( 2 + 4 + 6 +.... +100) + (50x3)
  
  2^2(1^2+2^2+3^2+....+50^2) + 2(1+2+3+.....+50)+ 50x3
  
  = 2 ^ 2 * ((50 * 51 * 101)/6) + 2((50 * 51)/2) + 50 * 3
  
  = 100 * 1717 + 50 * 54
  
  171700 + 2700
  
  =174400
  
  Therefore option A is the answer.
  
  Thank you 😊
  Happy Learning 😁
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