Reconstruct an arithmetic sequence
Haskell, 63 bytes



f(a:b:c)|s&lt;-[a,b..last c],all(`elem`s)c=s
f a=r$f$r a
r=reverse


Try it online!

Basically works by trying to build the result from the front and, if that fails, from the back. This uses the fact that the first and last members of the input will always be correct, the fact that deleted members have to be consecutive, and the fact that there will always be at least three items in the input. All I have to do is assume that the second or second-to-last members are accurate and check if it works. Luckily Haskell has really beautiful syntax for creating arithmetic series.

EDIT: thanks to @xnor for pointing out a bug and providing a solution!