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Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for th...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.
-24, 48, -96
Write your answer using decimals and integers.
an = __ (__)n-1
-24, 48, -96
Write your answer using decimals and integers.
an = __ (__)n-1
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Answered by
GPT-4o mini
To find the equation that describes the sequence \(-24, 48, -96\), we can start by examining the first few terms:
1. \( a_1 = -24 \)
2. \( a_2 = 48 \)
3. \( a_3 = -96 \)
### Identifying the Pattern
Let's observe how each term relates to the position \( n \):
- The first term is \(-24\).
- The second term is \( 48\) which is \(-24(−2)\).
- The third term is \(-96\) which is \(48(−2)\) or \(-24(−4)\).
### Finding a Formula
There appears to be a pattern in the signs and the magnitudes. Each term seems to alternate signs and is multiplied by a factor related to \( (-2) \).
From this observation, we can conclude that with each term, the value is multiplied by \(-2\) raised to the power of \( n - 1\).
#### General Formula
The general formula for this sequence can be expressed as:
\[
a_n = -24 \cdot (-2)^{n-1}
\]
### Final Answer
Thus, the equation to describe the sequence is:
\[
a_n = -24(-2)^{n-1}
\]
1. \( a_1 = -24 \)
2. \( a_2 = 48 \)
3. \( a_3 = -96 \)
### Identifying the Pattern
Let's observe how each term relates to the position \( n \):
- The first term is \(-24\).
- The second term is \( 48\) which is \(-24(−2)\).
- The third term is \(-96\) which is \(48(−2)\) or \(-24(−4)\).
### Finding a Formula
There appears to be a pattern in the signs and the magnitudes. Each term seems to alternate signs and is multiplied by a factor related to \( (-2) \).
From this observation, we can conclude that with each term, the value is multiplied by \(-2\) raised to the power of \( n - 1\).
#### General Formula
The general formula for this sequence can be expressed as:
\[
a_n = -24 \cdot (-2)^{n-1}
\]
### Final Answer
Thus, the equation to describe the sequence is:
\[
a_n = -24(-2)^{n-1}
\]
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