Q. What is the next number of the following sequence
21,77,165,285,......

• 21=5^2-4
  77=9^2-4
  165=13^2-4
  285=17^2-4
  5,9,13,17,21(+4)
  in the same way next no. will be
  21^2-4=441-4=437
• 10 years agoHelpfull: Yes(45) No(2)
• look series
  3*7=21
  7*11=77
  11*15=165
  15*19=285
  19*23=437 ans
  T(n)=(4n-1)*(4n+3)
  put value of n find any term...
  
• 10 years agoHelpfull: Yes(35) No(0)
• the common number is 32 look below...
  77 - 21 = 56
  165- 77 = 88
  285-165 = 120
  
  i.e, 56+32=88
  88+32=120
  120+32=152
  
  so after 120 the next difference number should be 152
  so the next number will be 285+152=437
  
  
• 10 years agoHelpfull: Yes(14) No(0)
• 21=5^2-4
  77=9^2-4
  165=13^2-4
  285=17^2-4
  5,9,13,17,21(+4)
  in the same way next no. will be
  21^2-4=441-4=437
  
  
  
• 10 years agoHelpfull: Yes(4) No(1)
• here in the series the difference of the difference of the numbers is 32.
  look below...
  77 - 21 = 46
  165- 77 = 88
  285-165 = 120
  
  88 - 46 = 42
  120- 88 = 32
  so next difference will be 22
  so next no. will be 120 + 32 + 285 = 437
  
• 10 years agoHelpfull: Yes(3) No(4)
• 3*7=21
  7*11=77
  11*15=165
  15*19=285
  19*23=437
• 10 years agoHelpfull: Yes(3) No(0)
• 77-21=56,165-77=88,285-165=120
  88-56=32
  120-88=32
  120+32=152
  285+152=437
• 10 years agoHelpfull: Yes(1) No(0)
• 4^2+5=21
  8^2+13=77
  12^2+21=165
  16^2+29=285
  20^2+37=437
• 10 years agoHelpfull: Yes(1) No(0)
• 4^2+5=21
  8^2+13 =77
  12^12+21 =165
  16^2+29 =285
  20^2+37 =437
  ans.437
• 10 years agoHelpfull: Yes(1) No(0)
• 77-21=56
  165-77=88
  285-165=120
  88-56=120-88=32
  then 120+32=152
  so 285+152=437
• 10 years agoHelpfull: Yes(1) No(0)
• 11*2=22 but 1 is less
  11*7=77
  11*15=165
  11*26=286 but 1 is less
  7-2=5
  15-7=8
  26-15=11 diff is 3 so
  next 11*40=440
• 10 years agoHelpfull: Yes(1) No(2)
• 4 ^ 2 + 4*1+1 =21
  8 ^ 2 + 4*3+1 = 77
  12 ^ 2 + 4*5+1 = 165
  16 ^ 2 + 4*7+1 = 285
  20 ^ 2 + 4*9+1 = 437
  ans>>>>>>next term will be 437
• 10 years agoHelpfull: Yes(1) No(0)
• Look upon series carefully
  
  21,77,165,285
  
  77 - 21 = 46
  165- 77 = 88
  285-165 = 120
  
  88 - 46 = 42
  120- 88 = 32
  so next difference will be 22
  so next no. will be 120 + 22_+ 285 = 427
• 10 years agoHelpfull: Yes(0) No(6)
• 285+152=437
• 10 years agoHelpfull: Yes(0) No(0)
• 8*19=152, 152+285=437
• 10 years agoHelpfull: Yes(0) No(0)
• 437....in the above series difference between each num follows the series..56,88(56+32),120(88+32)...
• 10 years agoHelpfull: Yes(0) No(0)
• 437
  21^2 - 4
• 10 years agoHelpfull: Yes(0) No(0)
• ANS: 437
  77-21=56 ;
  165-77=88 ;88-56=32
  285-165=120 ;120-88=32
  
  120+32=152
  so, 285+152=437
  
• 10 years agoHelpfull: Yes(0) No(0)
• 437
  77-21=56
  165-77=88 ;88-56=32
  285-165=120 ;120-88=32
  so next diff. 32
  120+32=152
  152+285=437
• 10 years agoHelpfull: Yes(0) No(0)
• 4^2+5
  4^3+13
  4^4+21
  4^5+29
  4^6+37
  
• 9 years agoHelpfull: Yes(0) No(0)
• 21..(56)......77...(88)...165...(120)....285...........(differences)
  " ......32..... " ......32..." add 32+120 =152
  finally add 285+152=437
  
• 9 years agoHelpfull: Yes(0) No(0)
• A.437
  first difference between the numbers will be
  77-21=56,165-77=88,285-165=120,x-285=?
  88-56=32,120-88=32
  add last difference values,i.e 32+120+285=437
  
• 9 years agoHelpfull: Yes(0) No(0)
• 21=5^2-4
  77=9^2-4
  165=13^2-4
  285=17^2-4
  next no. will be
  21^2-4=441-4=437
  
• 9 years agoHelpfull: Yes(0) No(0)
• 21=5^2-4
  77=9^2-4
  165=13^2-4
  285=17^2-4
  5,9,13,17,21(+4)
  so, 21^2-4=441-4=437
  
• 9 years agoHelpfull: Yes(0) No(0)
• 4^2+5
  4^3+13
  4^4+21
  4^5+29
  4^6+37
• 9 years agoHelpfull: Yes(0) No(1)
• 21,77,165,285.....
  77-21=56
  165-77=88
  285-165=120
  the difference btw 56 , 88 , 120 is 32 so we add 32 in 120
  e.g. 120+32=152
  ?-285=152 . so , ans is 437
• 5 years agoHelpfull: Yes(0) No(0)
• 77-21=56
  165-77=88
  285-165=120
  437-285=152
  88-56=32
  120-88=32
  152-120=32
  so ans is 437
• 4 years agoHelpfull: Yes(0) No(0)
• 3*7=21
  7*11=77
  11*15=165
  15*19=285
  19*23=437
• 3 years agoHelpfull: Yes(0) No(0)