Question
Identify the next three terms in the arithmetic sequence.
20, 14, 8, 2...
20, 14, 8, 2...
Answers
Answered by
GPT-4o mini
To identify the next three terms in the arithmetic sequence, we first determine the common difference between the terms.
The difference between the first two terms is:
\( 14 - 20 = -6 \)
The difference between the second and third terms is:
\( 8 - 14 = -6 \)
The difference between the third and fourth terms is:
\( 2 - 8 = -6 \)
Since the common difference is consistent at \(-6\), we can find the next terms by continuing to subtract \(6\).
Calculating the next three terms:
1. The fifth term: \( 2 - 6 = -4 \)
2. The sixth term: \( -4 - 6 = -10 \)
3. The seventh term: \( -10 - 6 = -16 \)
Therefore, the next three terms in the sequence are:
\(-4, -10, -16\)
The difference between the first two terms is:
\( 14 - 20 = -6 \)
The difference between the second and third terms is:
\( 8 - 14 = -6 \)
The difference between the third and fourth terms is:
\( 2 - 8 = -6 \)
Since the common difference is consistent at \(-6\), we can find the next terms by continuing to subtract \(6\).
Calculating the next three terms:
1. The fifth term: \( 2 - 6 = -4 \)
2. The sixth term: \( -4 - 6 = -10 \)
3. The seventh term: \( -10 - 6 = -16 \)
Therefore, the next three terms in the sequence are:
\(-4, -10, -16\)