Find the 100th term of the following series - 3,6,12,21,33,48...

• The given series i.e 3,6,12,21,33......
  is derived from a(n+1)=a(n)+3n for n>0
  where a(1)=3
  now a(99+1)=a(100)=a(99)+3*99
  a(98+1)=a(99)=a(98)+3*98
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  a(1+1)=a(2)=a(1)+3*1
  
  therefore
  a(100)=a(99)+3*99
  a(100)=a(98)+3*98+3*99
  a(100)=a(97)+3*97+3*98+3*99
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  continue in this way
  finaly we get
  a(100)=a(1)+3*1+3*2+3*3+.................+3*99
  =3+ 3(1+2+3+4+5+6+7+8.....+99)
  =3+3(sum of 99 A.P terms)
  =3+3(99x100)/2
  =14,853
  
• 11 years agoHelpfull: Yes(27) No(3)
• 14853.
  1st term=3
  2nd term=3+3*1
  3rd term=3+3*1+3*2
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  100th term=3+3*1+3*2.........+3*99
  =3+3{1+2+3+.......99}
  =3+3{(100*99)/2}
  =14853
  
• 11 years agoHelpfull: Yes(26) No(1)
• 3=3*1;
  6=3*(1+1);
  12=3*(1+1+2);
  21=3*(1+1+2+3);
  33=3*(1+1+2+3+4);
  48=3*1(1+1+2+3+4+5)& so on.. now the 100th term should b equal to=3*(1+the sum of (100-1)th natural no i.e.99*100/2=4950)=14853
• 11 years agoHelpfull: Yes(6) No(0)
• 3 6 12 21 33 48
  take 3 common( 1 2 4 7 11 16.....)
  now see the diff b/w no's (1 2 3 4 5.....)
  now apply A.P formula tn=a+(n-1)d
  t100= 1+(100-1)1
  t100=100
  now multiply that 3 which we took common so ans is 300
• 11 years agoHelpfull: Yes(5) No(19)
• @sakthi..u r finding the 100th term for series of common differences and not for the given series!!...we get 100th term in common difference as 100
• 11 years agoHelpfull: Yes(3) No(1)
• ans should be 14853
  because t(n+1)=t(n)+3(n-1)
• 11 years agoHelpfull: Yes(3) No(1)
• 14853 is the right answer
• 11 years agoHelpfull: Yes(3) No(0)
• ans is 15153
• 11 years agoHelpfull: Yes(2) No(6)
• its adiing like..
  3,6,9..
  so last term will be 48+18=66
• 11 years agoHelpfull: Yes(1) No(7)
• 3+3*0=3
  3+3*0+3*1=6
  3+3*0+3*1+3*2=12
  3+3*0+3*1+3*2+3*3=21
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  3+3(1+2+3+....+99)
  3+3((99*(99+1)/2))
  3+14850
  14853...ans
• 8 years agoHelpfull: Yes(1) No(0)
• vivek garu can u expn ur aans plzzzz????
• 11 years agoHelpfull: Yes(0) No(3)
• SAGAR , s i'm wrong, thanks for ur feedback
• 11 years agoHelpfull: Yes(0) No(0)
• ans is 66
  
• 11 years agoHelpfull: Yes(0) No(0)