The sum of 51 terms of the A.P. whose second term is 2 and the 4th term is 8 is ____.

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Accepted Answer

The sum of 51 terms of the A.P. whose second term is 2 and the 4th term is 8 is 3774.Given an A.P. whose second term is 2 and the 4th term is 8 .We know,The sum of 1st n terms of an AP is given by

S
    n
   
   =
    n
    2

2a+
      
       n−1
     d
   
  .nth term of an AP is given by

a
    n
   
   =a+
    
     n−1
   d
  .Where,The first term is a.The common difference is d.The number of terms are n.The second term is,

a
      n
     
     =a+
      
       n−1
     d

⇒2=a+
      
       2−1
     d

⇒a+d=2

⇒a=2−d

……(1)The 4th term is,

a
      n
     
     =a+
      
       n−1
     d

⇒8=a+
      
       4−1
     d

⇒a+3d=8

……(2)The common difference will be,(2-d)+3d=8⇒2-d+3d=8⇒2d=6⇒d=3The first term will be,

a=2−d

⇒a=2−3

⇒a=−1

Hence, the sum will be,

S
      n
     
     =
      n
      2

2a+
        
         n−1
       d

⇒
      S
      
       51
     
     =
      
       51
      2

2
        
         −1
       +
        
         51−1
       3

⇒
      S
      
       51
     
     =
      
       51
      2

−2+50×3

⇒
      S
      
       51
     
     =
      
       51
      2

−2+150

⇒
      S
      
       51
     
     =
      
       51

2

×14
      
       8

74

⇒
      S
      
       51
     
     =51×74

⇒
      S
      
       51
     
     =3774

Therefore, the sum is

S
    
     51
   
   =3774
  .

The sum of 51 terms of the A.P. whose second term is 2 and the 4th term is 8 is ____.

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