Question

What is a31 of the arithmetic sequence for which a5=12.4 and a9=22.4

Answer 1

For the arithmetic sequence
a₁, a₂, a₃, ...,
the n-th term is
$a_{n}=a_{1}+(n-1)d$
where d =  the common difference

Because a₅ = 12.4,
a₁ + 4d = 12.4           (1)
Because a₉ = 22.4,
a₁ + 8d = 22.4          (2)

Subtract (1) from (2).
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
d = 2.5
From (1),
a₁ = 12.4 - 4*2.5 = 2.4

Therefore
a₃₁ = 2.4 + 30*2.5 = 77.4

Answer:  a₃₁ = 77.4