Question

The 9th term of an AP is 499 and 499th term is 9.Find the term which is equal to zero

Answer 1

Hi Mate !!


a ( First term )

d ( Common difference )

n ( no. of term )

an ( nth term )

• an = a + ( n - 1 )d


• Given :- 9th term is 499 i.e ,

a9 = 499 ..... ( When n = 9 ) ..... ( i )

499th term is 9 i.e ,

a499 = 9 ..... ( When n = 499 ) .... ( ii )

From ( i )

a9 = 499

a + 8d = 499 .... ( iii )

From ( ii )

a499 = 9

a + 498d = 9 ...... ( iv )

Subtracting ( iv ) from ( iii )

a + 8d - ( a + 498d ) = 499 - 9

a + 8d - a - 498d = 490

- 490d = 490

d = ( - 1 )


Putting value of d in eq ( iii )

a + 8d = 499

a + 8 × ( - 1 ) = 499

a - 8 = 499

a = 499 + 8

a = 507

Now , we have value of a and d , value of an is already given i.e, 0 ( Zero ) and we have to find value of n !!

As ,

an = a + ( n - 1 ) d

0 = 507 + ( n - 1 ) × ( - 1 )

0 = 507 - n + 1

0 = 508 - n

- 508 = - n

n = 508 !!


Hence , the value of an at n = 508 will be Zero !!


° Verification :-

an = a + ( n - 1 ) × d

an = 507 + ( 508 - 1 ) × ( - 1 )

an = 507 + 507 × ( - 1 )

an = 507 - 507

an = 0

Hence , verified !!

Answer 2

508 is the answer.....