Question

Consider the sequence 1, 4, 16, 64, 128, … Which statement describes the sequence? The sequence diverges. The sequence converges to 0. The sequence converges to [infinity]. The sequence converges to –[infinity].

Answer 1

The sequence diverges

Explanation:

The given sequence is 1, 4, 15, 64, 128, ...

By observation the sequence can be expressed as a sequence of 4 raised to increasing powers of 'x' as follows;

The sequence is 4ˣ, where; x = 0, 1, 2, 3, 4, ..., ∞

Therefore, the values of each subsequent term of the sequent is higher than the term it succeeds, the sequence does not converge to a given limit value and therefore, the sequence diverges.