Question

If 9th term ofap is 99 and 99th term is 9 which term is zero]​

Answer 1

Answer:

108 th term is zero

Step-by-step explanation:

The nth term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₉ = 99 and a₉₉ = 9 then

a₁ + 8d = 99 → (1)

a₁ + 98d = 9 → (2)

Subtract (1) from (2) term by term to eliminate a₁

0 + 90d = - 90

90d = - 90 ( divide both sides by 90 )

d = - 1

Substitute d = - 1 into (1) for value of a₁

a₁ + 8(- 1) = 99

a₁ - 8 = 99 ( add 8 to both sides )

a₁ = 107

Then

107 - (n - 1) = 0

107 - n + 1 = 0

- n + 108 = 0 ( subtract 108 from both sides )

- n = - 108 ( multiply both sides by - 1 )

n = 108

The 108th term is zero