The sum of the first 35 terms of an A.P, if the second term is 2 and the seventh term is 22 is ____.

Question

Accepted Answer

The sum of the first 35 terms of an A.P., if the second term is 2 and the seventh term is 22 is 2310.Given that,Second term is 2 and the seventh term is 22.The sum of the arithmetic progression is given as,

S
    n
   
   =
    n
    2

2a+
      
       n−1
     d
   .
  Where,The first term is a.The common difference is d.The number of terms are n.According to the question,

a
    2
   
   =2

n=35
  . The second term of A.P can be represented as

a

2

=a+d
  . Substitute 2 for

a
    2

in

a
    2
   
   =a+d
   to obtain the equation in terms of a and d,

a
      2
     
     =a+d

⇒2=a+d

⇒a=2−d

Again, The seventh term of A.P can be represented as

a

7

=a+6d
  . Substitute 22 for

a
    7

in

a
    7
   
   =a+6d
   to obtain the equation in terms of a and d.

a
      7
     
     =a+6d

⇒22=a+6d

Now, the common difference will be,

22=a+6d

⇒22=2−4+6d

⇒22=−2+6d

⇒6d=22+2

⇒6d=24

⇒d=4

Therefore,

2=a+d

⇒2=a+4

⇒a=−2

Hence, the sum will be,

S
      
       35
     
     =
      
       35
      2

2
        
         −2
       +
        
         35−1
       4

⇒
      S
      
       35
     
     =
      
       35
      2

−4+34
        4

⇒
      S
      
       35
     
     =
      
       35
      2

−4+136

⇒
      S
      
       35
     
     =
      
       35
      2

132

⇒
      S
      
       35
     
     =35
      
       66

⇒
      S
      
       35
     
     =2310

Therefore, the sum of the first 35 terms of an A.P is 2310.

The sum of the first 35 terms of an A.P, if the second term is 2 and the seventh term is 22 is ____.

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