7: The sequence goes
a₀ = −1,
a₁ = 3,
a₂ = −2,
a₃ = 11.

When n tends to infinity, the term 2ⁿ in the sequence prevails (see intuitive calculation). It goes to infinity, but it is modified by the alternating term (−1)ⁿ. Thus in the sequence we are getting numbers that grow in absolute value but keep changing sign; that is, the sequence oscillates and the size of oscillation increases to infinity.

Next hint - boundedness
Next hint - monotonicity
Answer