Question

IF THE 7TH TERM OF AN AP IS 1 BY 9 AND IS 9TH TERM IS 1 BY 7 ITS 64th term​

Answer 1

Answer:

it is high level question so I will not be able to tell you

Answer 2

Answer:

64 / 63

Step-by-step explanation:

nth term of any AP is given by a + ( n - 1 )d, where a is the first term and d is the common difference between the terms.

 Here, let the first term be a and common difference be d.

⇒ 7th term = 1 / 9

⇒ a + ( 7 - 1 )d = 1 / 9

⇒ a + 6d = 1 / 9

⇒ a = 1 / 9 - 6d

      ⇒ 9th term = 1 / 7

⇒ a + ( 9 - 1 )d = 1 / 7

⇒ a + 8d = 1 / 7

     Value of a from above,

⇒ 1 / 9 - 6d + 8d = 1 / 7        

⇒ 8d - 6d =  1 / 7 - 1 / 9

⇒ 2d = ( 9 - 7 ) / 63

⇒ 2d = 2 / 63

⇒ d = 1 / 63

Hence,

          a = 1 / 9 - 6d

           = 1 / 9 - 6 / 63

           = ( 7 - 6 ) / 63

           = 1 / 63

Therefore,

  ⇒ 64th term

   = 1 / 63 + ( 64 - 1 )( 1 / 63 )

   = 1 / 63 + ( 63 )( 1 / 63 )

   = 1 / 63 + 1

   = ( 1 + 63 ) / 63

   = 64 / 63