Question

The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is

विकल्प

• 501^th

• 502^th

• 508^th

• none of these

Answer 1

In the given problem, let us take the first term as a and the common difference as d.

Here, we are given that,

`a_9 = 449`                   ...............(1) 

`a_449 = 9 `                 .................(2) 

We need to find n

Also, we know,

`a_n = a + ( n- 1) d`

For the 9^th term (n = 9),

   `a_9 = a + ( 9 -1) d`

449 = a + 8d                   (Using 1 ) 

   a = 449 - 8 d                 .................(3) 

Similarly, for the 449^th term (n = 449),

`a_449 = a + ( 449 - 1 )d`

     9 = a + 448d                 (Using 2 ) 

     a = 9 - 448 d                   .............(4) 

Subtracting (3) from (4), we get,

a -a  = ( 9 - 448d) - ( 449 - 8d) 

    0 = 9 - 448d - 449  + 8d

    0 = -440 - 440d

440d = - 440

      d = - 1

Now, to find a, we substitute the value of d in (3),

a = 449 - 8 (-1) 

a = 449 + 8

a = 457

So, for the given A.P  d = - 1 and a = 457

So, let us take the term equal to zero as the n^th term. So,

`a_n = 457 + ( n- 1) ( -1 ) `

   0 = 457 - n + 1

   n = 458

So,   n = 458