Q. What will be the next number?
1,6,21,52,105,186,...

• Look upon the series carefully;
  1,6,21,52,105,186,...
  
  6 - 1 = 5
  21 - 6 = 15
  52 - 21 = 31
  105- 52 = 53
  186- 105= 81
  
  5 , 15 , 31 , 53 ,81
  15 - 5 = 10
  31 -15 = 16
  53 -31 = 22
  81 -53 = 28
  
  10 , 16 ,22 ,28
  each no. has the difference of 6
  so the next number of this series will be
  
  28 + 6 = 34
  34 + 81 = 115
  add this with last no.
  186 + 115 = 301
  so next no will 301
  
• 10 years agoHelpfull: Yes(5) No(1)
• 1,6,21,52,105,186,301
  
  a(n) = n^3 - n^2 + n
  a(1)=1-1+1=1
  a(2)= 8-4+2=6
  a(3)= 27-9+3=21
  ..
  ..
  a(7)= 7^3-7^2+7= 7(7^2-7+1)=7*43= 301
• 10 years agoHelpfull: Yes(4) No(0)
• i dont know
• 3 years agoHelpfull: Yes(0) No(1)