[tex]a_n=a_1+(n-1)d[/tex] - the formula of n-th term of an arithmetic sequence.
We have:
[tex]a_5=12.4;\ a_9=22.4[/tex]
[tex]a_9-a_5=(9-5)d\to4d=22.4-12.4\\\\4d=10\ \ \ \ |:4\\\\d=2.5[/tex]
[tex]a_{31}=a_9+(31-9)d\to a_{31}=22.4+22\cdot2.5=77.4[/tex]
Answer: C. 77.4
