-2,4,-8,16,

Pattern: Each term is multiplied by -2 to obtain the next term. This is a geometric sequence with a common ratio of -2.

General Formula:

The ( n )-th term can be expressed as:

[

a_n = (-2)^n

]

Next Term: Following the pattern, the term after 16 is:

[

16

imes (-2) = -32

]

Sequence Explanation:

1. Start with (-2).

2. Multiply by (-2): (-2

imes -2 = 4).

3. Multiply by (-2): (4

imes -2 = -8).

4. Multiply by (-2): (-8

imes -2 = 16).

5. Continue this pattern: (16

imes -2 = -32), and so on.

Key Insight: The sequence alternates in sign and doubles in magnitude each time due to the common ratio of (-2).