Haskell, 35 bytes

g l@(a:b:c)=zipWith(-)c l==b:init c

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Haskell, 34 bytes

g(a:l@(b:c:_))=a+b==c&&g l;g _=0<1

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• Thanks to @Laikoni for suggesting a recursive approach 1 Byte shorter

• Original solution 35 bytes

g l@(a:b:c)=zipWith(-)c l==b:init c

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