Answer:
a₁₃ = - 20
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂ = 13 and a₄ = 7 , then
a₁ + d = 13 → (1)
a₁ + 3d = 7 → (2)
Subtract (1) from (2) term by term to eliminate a₁
2d = - 6 ( divide both sides by 2 )
d = - 3
Substitute d = - 3 into (1)
a₁ - 3 = 13 ( add 3 to both sides )
a₁ = 16
Then
a₁₃ = 16 + (12 × - 3) = 16 - 36 = - 20
