Final answer:
The pattern in the sequence -2, 4, -8, 16 is each term multiplied by -2, which is option A) Multiply by -2. Using this rule, the next terms are -32 and 64 respectively, and the expression for the pattern is an = a1 × (-2)^{n-1}.
Step-by-step explanation:
The pattern in the sequence -2, 4, -8, 16, __, __ is that each term is the previous term multiplied by -2. This can be seen in the sequence as every time we move to the next number, it changes sign (positive to negative or vice versa) and the absolute value doubles. The first term is -2, and when we multiply this by -2, we get 4. When we multiply 4 by -2, we get -8, and similarly, -8 multiplied by -2 gives us 16.
Therefore, the correct option to describe the pattern is A) Multiply by -2.
Additionally, we need to apply the same rule to continue the sequence. Given the last known term in the sequence is 16, the next terms would be:
- 16 × (-2) = -32
- -32 × (-2) = 64
In mathematical terms, if we call the first term a1 and subsequent terms an, where n is the term number in the sequence, the expression for the pattern can be an = a1 × (-2)^{n-1}.