Python 3, 37 bytes

Outputs by failing/not failing.

f=lambda a,*b:b>()>(2*a>b[0]>q,f(*b))

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Python 3, 40 bytes

f=lambda a,*b:b==()or 2*a<=b[0]and f(*b)

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Python 3, 37 29 bytes

-8 bytes thanks to xnor.

Fails for doubling sequences, completes otherwise.

f=lambda a,*b:2*a<=b[0]>f(*b)

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Python 3, 40 bytes

f=lambda a,*b:b==()or 2*a<=b[0]and f(*b)

Try it online! Test suite by Noodle9.

Python 3, 40 bytes

f=lambda a,*b:b==()or 2*a<=b[0]and f(*b)

Try it online!

Python 3, 37 bytes

Outputs by failing/not failing.

f=lambda a,*b:b>()>(2*a>b[0]>q,f(*b))

Try it online!

Python 3, 40 bytes

f=lambda a,*b:b==()or 2*a<=b[0]and f(*b)

Try it online! Test suite by Noodle9.