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

Question

Philoid · Accepted Answer

Here, a₉ = 449

A₄₄₉ = 9

Let a is the first term and d is the common difference of the AP

Given 9th term of AP = 499

a + 8d = 499 .....(1)

Again 499th term of AP = 9

a + 498d = 9 .....(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 = 499

a = 499 + 8

a = 507

Let nth term is equal is to zero

a + (n–1)d = 0

507 – (n–1) = 0 (By putting value of a and d)

507 – n + 1 = 0

508 – n = 0

n = 508

So 508^th term of AP is zero.