Answer:
the whole sequence is
5, 1 1/2, -2, -5 1/2, -9
the missing elements were
1 1/2, -2, -5 1/2
Explanation:
an arithmetic sequence means that there is always constant added or subtracted from the previous term to create the next term.
we know, we need to go 4 steps or terms to get from 5 to -9.
5 + c = ?
5 + c + c = ??
5 + c + c + c = ???
5 + c + c + c + c = -9
5 + 4c = -9
4c = - 14
c = -14/4 = -7/2
so, we get
? = 5 + -7/2 = 10/2 - 7/2 = 3/2 = 1 1/2
?? = 3/2 - 7/2 = -4/2 = -2
??? = -4/2 - 7/2 = -11/2 = -5 1/2
and the next step is -11/2 - 7/2 = -18/2 = -9
correct.