Question

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

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Answer 1

Answer:

a+8d=499

a+498d=9

-490d=490

d=-1

a=507

0=507+(n-1)d

-507/-1=n-1

507+1=n

508 is the term

Answer 2

Heyy dear♥️

The term which is equal to zero is 508

SOLUTION :

We know that, a is the first term and d is the common difference of an AP.

Given: 9th term of AP = 499

⟹ a + 8d = 499 ‎ (say equation 1)

Again 499th term of AP = 9

⟹ a + 498d = 9‎ ( say equation 2)

Now subtract equation 1 and 2, we get

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

⟹ ‎‎a + 8d - a - 498d = 499 - 9

⟹ -490d = 490

⟹ d = -490/490

⟹ d = -1

Put value of d in equation1, we get

a + 8(-1) = 499

⟹ a - 8 = 499

⟹ a = 499+8

⟹ a = 507

Let nth term is equal is to zero

⟹ a + (n-1)d = 0

⟹ 507 - (n-1) = 0 (putting value of a and d)

⟹ 507 - n +1 = 0

⟹ 508 - n = 0

⟹ n = 508

Hence 508th term of AP is equal to zero.

VERIFICATION :

an = a + (n - 1) × d

an = 507 + (508 - 1) × (-1)

an = 507 + 507 × (-1)

an = 507 - 507

an = 0

HENCE PROVED

Hope you got it :)