87th number in the series 2, 10, 26, 50…….

• Observing the given we can write the following :
  
  
  2nd term - 1st term = 1*8;
  3rd term - 2nd term = 2*8;
  4th term - 3rd term = 3*8;
  5th term - 4th term = 4*8;
  .
  .
  .
  (n-1)th term - (n-2)th term =(n-2)*8
  (n)th term - (n-1)th term =(n-1)*8;
  ---------------------------------------------
  Summing up all the above terms we get ,
  (n)th term - 1st term = {1+2+......+(n-1)}*8
  =>(n)th term = 8*{n*(n-1)}/2 + 1st term
  =>(n)th term = 8*{n*(n-1)}/2 +2;
  So, Clearly 87th term of the sequence will be :
  8*{n*(n-1)}/2 +2 = 8*{87*86}/2 +2 = 4*86*87 +2 = 29930
  
  Hence, 87th term will be : 29930
• 11 years agoHelpfull: Yes(121) No(10)
• answer is =29930
  series is 2,10,26,50
  like 1st term is 2 = 1^2+1
  2nd term is 10= 3^2+1
  3rd term is 26= 5^2+1
  similarly 87 term is = 173^2+1=29930......
  as we seen above that in 1st ,2nd,& 3rd term it is squire of corresponding odd numbers+1
  since 1st odd no is 1(1*2-1),,,,,2nd odd no is 3 (2*2-1),,,,3rd odd no is 5(2*3-1).....similarly 87 odd no is (2*87-1)= 173......
• 11 years agoHelpfull: Yes(76) No(4)
• Sorry for the wrong ans 29930 is correct.
  when diff are in AP
  Nth term = an^2 + bn +c
  
  put a + b + c = 2
  4a + 2b + c = 10
  9a + 3b + c +26
  a = 4
  b = -4
  c = 2
  Lil trick i learnt in 12th
  now put n = 87
  ans = 29930
• 11 years agoHelpfull: Yes(16) No(4)
• 1st =2
  2nd =2+1*8
  3rd=2+1*8+2*8
  4th=2+1*8+2*8+3*8
  .....
  ....
  nth=2+1*8+2*8+....+(n-1)*8, then
  87th=2+1*8+2*8....(87-1)*8
  87th=2+(87/2)*{2*1+(87-1)*8}
  =2+29928
  =29930
• 11 years agoHelpfull: Yes(12) No(0)
• ans is 690..
  the gn series is of the form a,a+d,a+2d,a+3d....,a+nd...
  here n=87
  a+(n-1)d
  2+(86*8)
  -->690
  
• 11 years agoHelpfull: Yes(7) No(35)
• 1st =2
  2nd =2+1*8
  3rd=2+1*8+2*8
  4th=2+1*8+2*8+3*8
  .....
  ....
  nth=2+1*8+2*8+....+(n-1)*8, then
  87th=2+1*8+2*8....(87-1)*8
  87th=2+(86/2)*{2*8+(86-1)*8}
  =2+29928
  =29930
• 11 years agoHelpfull: Yes(4) No(0)
• //sorry for previous wrong calculation
  
  series is 2,10,26,50,...
  to find t(87)
  now 2, 10, 26, 50
  common difference ---> 8 16 24
  again c.d ----> 8 8
  
  so T(n)=a(n-1)*(n-2)+b(n-1)+c
  now put n=1,2,3
  T(1)=c=2 ----(i)
  T(2)=b+c=10 ----(ii)
  T(3)=2a+2b+c=26--(iii)
  from (i),(ii),(iii)
  a=4,b=8,c=2
  
  now u can calculate any term of the progression from above expression
  T(n)=a(n-1)*(n-2)+b(n-1)+c
  
  so T(87)=4*86*85+8*86+2=29930 Ans.
  
  one can verify it by
  T(5) = 4*4*3 + 8*4 +2
  =82
• 11 years agoHelpfull: Yes(3) No(1)
• 2, 10, 26, 50
  10-2=8
  26-10=16
  50-26=24
  next no should be a 82
  82-50=32
• 11 years agoHelpfull: Yes(2) No(20)
• series is 2,10,26,50,...
  to find t(87)
  now 2, 10, 26, 50
  common difference ---> 8 16 24
  again c.d ----> 8 8
  
  so T(n)=a(n-1)*(n-2)+b(n-1)+c
  now put n=1,2,3
  T(1)=c=2 ----(i)
  T(2)=b+c=10 ----(ii)
  T(3)=2a+2b+c=26--(iii)
  from (i),(ii),(iii)
  a=4,b=8,c=2
  
  now u can calculate any term of the progression from above expression
  T(n)=a(n-1)*(n-2)+b(n-1)+c
  
  so T(87)=4*86*85+8*86+2=688 Ans.
  
  one can verify it by
  T(5) = 4*4*3 + 8*4 +2
  =82
  
  
• 11 years agoHelpfull: Yes(2) No(1)
• 2 = 12 + 1
  10 = 32 +1
  26 = 52 + 1
  50 = 72 + 1
  Now,
  1,3, 5, 7 ...... forms a AP series with common difference 2.
  So, we will find T87 firs through Ap.
  Tn = a +(n-1)*d
  Tn = 1 + (87 -1) *2 = 1 + 86 *2 = 173.
  Now,
  87th term = 1732 + 1 = 29929 + 1 = 29930.
• 7 years agoHelpfull: Yes(2) No(0)
• a=2,d=8,n=87
  a+(n-1)d
  2+(86*8)
  690 ans
  
• 11 years agoHelpfull: Yes(1) No(11)
• The difference = 8
  8,16,24
  the 87th difference is
  8+(87-1)8
  = 696
  
  So 2-10-26
  then 2+696 = 698 should be the ans , not sure though
• 11 years agoHelpfull: Yes(1) No(10)
• the series is 2 10 26 50... from this series we got a series of multiple of 8
  8 16 24 32
  now we have 2 find 87th number in the 1st series means 86 in the 2nd series.
  from the formula-> Tn=a+(n-1)*d
  we got Tn=8+(85*8)=688
  Now just sum the all terms from the formula Sn=(n/2)*[2a+(n-1)*d]
  we got Sn=29928 and this is the answer
• 11 years agoHelpfull: Yes(1) No(3)
• LALA JI Best solution... :)
• 9 years agoHelpfull: Yes(0) No(1)
• Its in the for ar^n
• 7 years agoHelpfull: Yes(0) No(0)
• The series is made up of addition of the previous term with multiples of 8.
  First term: 2 + 8(0) = 2
  Second term: First term + 8(1) = 2+8 =10
  Third term = Second term + 8(2) = 10 + 16 = 26
  Fourth term : Third term + 8(3) = 26 + 24 = 50
  
  Can you see the pattern yet? We can generalize it to :
  
  g(n) = g(n-1) + (n-1)(8)
  If you try putting the values, such as n=3 (third term), you'll get
  g(3) = g(2) + (2)(8). We know that g(2) (second term) is equal to 10.
  Thus g(3) = 10 + 16 = 26.
  
  The question is for 87th term.
  g(87) = g(86) + 8(86)
  But do we know g(86) ? No, we don't. But we can find it out.
  Lets get back to the general equation.
  
  g(n) = g(n-1) + (n-1)(8)
  Substituite g(n-1) = g(n-2) + (n-2)(8)
  Thus, g(n) = g(n-2) + (n-1)8 + (n-2)(8)
  Similarly, substiute, g(n-2) = g(n-3) + (n-3)8
  .
  .
  .
  g(n) = g(1) + 8(n-1) + 8(n-2) + 8(n-3) + 8(n-4)..... 8(n-(n-1))
  We didn't know the 86th term. But we do know the 1st term i.e. g(1) = 2
  g(n) = 2 + 8[ n-1 + n-2 + n -3+..... n-n+1]
  g(87) = 2 + 8 [86 + 85 + 84 + 83+....1]
  1+2+3+4+....86 is a series with common difference = 1 and first term = 1. The sum of this type of series is n(n+1)/2 i.e (87)(86)/2.
  
  Therefore,
  g(87) = 2 + [8(86)(87)/2]
  g(87) = 2 + [59856/2]
  g(87) = 2 + 29928
  g(87) = 29930
• 5 years agoHelpfull: Yes(0) No(0)