Two terms of the AP: –15, –13, –11, … makes the sum as –55.

State true (T) or false (F).

Question

Two terms of the AP: –15, –13, –11, … makes the sum as –55.State true (T) or false (F).

Accepted Answer

The given AP series is –15, –13, –11, … .According to the question, a= -15 and,

d=−13−
      
       −15

=−13+15

=2

Now, as sum is -55, let’s find no. of terms by using the formula,

S
      n
     
     =
      n
      2

2a+
        
         n−1
       d

−55=
      n
      2

2
        
         −15
       +
        
         n−1
       2

−55
      2
     =n
      
       −30+2n−2

−110=n
      
       2n−32

2
      n
      2
     
     −32n+110=0

n
      2
     
     −16n+55=0

n
      2
     
     −11n−5n+55=0

n
      
       n−11
     −5
      
       n−11
     =0

n−5

n−11
     =0

n=5,11

Now, let’s obtain the sum of 5 terms and 11 terms to verify the result.  For n = 11,

S
      
       11
     
     =
      
       11
      2

2
        
         −15
       +
        
         11−1
       2

=
      
       11
      2

−30+20

=
      
       11
      2

−10

=−55

For n = 5,

S
      5
     
     =
      5
      2

2
        
         −15
       +
        
         5−1
       2

=
      5
      2

−30+8

=
      5
      2

−22

=−55

As, the sum of both 5 terms and 11 terms is equal to -55. Therefore, the given statement, “Two terms of the AP: –15, –13, –11, … makes the sum as –55.” is true.

Two terms of the AP: –15, –13, –11, … makes the sum as –55.

State true (T) or false (F).

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