Answer:
fifth term
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = 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