Question

If 9 times the 9th term of an ap is equal to 13 times its 13th term ,show that the 22nd term of an ap is zero

Answer 1

9a9 = 13a13 
9 (a + 8d ) = 13 (a + 12 d )
9a + 72d = 13a + 156d 
9a - 13a = 156d - 72d 
-4a = 82d 
a = -41d / 2
a22 = a+ 21d 
       =- 41d/ 2 +21d 
        -41d +41d /2
      = 0

Answer 2

9a9 = 13a13  

9 (a + 8d ) = 13 (a + 12 d )

9a + 72d = 13a + 156d  

9a - 13a = 156d - 72d  

-4a = 84d  

a = -21d

a22 = a+ 21d  

      =- 21d +21d  

          = 0