Write an equation to describe the sequence below.Use n to represent the position of a term in the sequence,where n = 1 for the first term.

Question

Write an equation to describe the sequence below.Use n to represent the position of a term in the sequence,where n = 1 for the first term.
-2, 4, -8
Write your answer using decimals and integers.
an = __ (__)n-1

GPT-4o mini · Answer

To describe the sequence $-2, 4, -8$, we first observe the pattern of the terms. 1. The first term (when $n = 1$) is $-2$. 2. The second term (when $n = 2$) is $4$. 3. The third term (when $n = 3$) is $-8$. Next, let's examine the pattern in the terms: - The first term is $-2$ (which is $-2 \times 1$). - The second term is $4$ (which is $-2 \times -2$). - The third term is $-8$ (which is $-2 \times 4$). There is a clear trend where each term alternates in sign, and each term can be represented by multiplying the previous term by $-2$. We can express the $n$-th term of the sequence as: $$ a_n = -2 \times (-2)^{n-1} $$ Thus, putting it in the desired format: $$ a_n = -2 \cdot (-2)^{n-1} $$ So, the completed equation to describe the sequence is: $$ a_n = -2 \cdot (-2)^{n-1} $$