State True/False.If the sum of first n term of an AP is

S
n

=2n−3
n
2

whose nth term is 5-6n, then the sum of its first 20 terms is -1160.Topic Introduction to Arithmetic Progressions

Question

State True/False.If the sum of first n term of an AP is

S
    n
   
   =2n−3
    n
    2

whose nth term is 5-6n, then the sum of its first 20 terms is -1160.Topic Introduction to Arithmetic Progressions

Accepted Answer

Given that,

S
    n
   
   =2n−3
    n
    2

.Formula for the

n
    
     th

term:

a
    n
   
   =a+
    
     n−1
   ×d

Consider 
      a
      n

be the n
      
       th 
     
      term of AP

∴
      a
      n
     
     =5−6n

Substitute n=1 and calculate 
      1
      
       st 
     
      term:

∴
      a
      1
     
     =5−6×1

⇒
      a
      1
     
     =−1

Substitute n=2 and calculate the 
      2
      
       nd 
     
      term:

∴
      a
      2
     
     =5−(6×2)

⇒
      a
      2
     
     =−7

Let d be the common difference of the AP:

∴d=
        a
        2
       
       −
        a
        1

⇒d=−7−(−1)

=−7+1

=−6

Determining the sum of first 20 terms of the AP by putting the values in equation (1),

S
    n
   
   =2n−3
    n
    2
   
   [given]

∴
        S
        
         20

=2×20−3×
        
         20
        2

⇒
        S
        
         20

=40−1200

=−1160

Therefore, the sum of the first 20 terms of the AP is -1160.Thus, the given statement is true.Hence, option (1) is correct.

State True/False.

If the sum of first n term of an AP is $S n = 2 n − 3 n 2$ whose nth term is 5-6n, then the sum of its first 20 terms is -1160.

Topic Introduction to Arithmetic Progressions