For the arithmetic sequence
a₁, a₂, a₃, ...,
The n-th term is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
where d = common difference.
Because a₁₀ = 41,
a₁ + 9d = 41 (1)
Because a₁₅ = 61
a₁ + 14d = 61 (2)
Subtract (1) from (2).
5d = 20
d = 4
From (1), obtain
a₁ = 41 - 9*4 = 5
Therefore
a₃ = 5 + 2*4 = 13
Answer: a₃ = 13
