Question

If the 3rd and 9th term of an ap are 4 and -8 respectively then which term of AP is zero​

Answer 1

Answer:

fifth term

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 4 and a₉ = - 8 , then

a₁ + 2d = 4 → (1)

a₁ + 8d = - 8 → (2)

Subtract (1) from (2)

6d = - 12 ( divide both sides by 6 )

d = - 2

Substitute d = - 2 into (1)

a₁ + 2(- 2) = 4

a₁ - 4 = 4 ( add 4 to both sides )

a₁ = 8

Thus equating the n th term formula to zero and solving for n

8 - 2(n - 1) = 0 ( subtract 8 from both sides )

- 2(n - 1) = - 8 ( divide both sides by - 2

n - 1 = 4 ( add 1 to both sides )

n = 5

The fifth term is equal to zero