Question
10:12 LTE Done docs.google.com Option 3 Option 4 5. * 20 points What is the common difference of the arithmetic sequence below? \[ -7 x,-4 x,-x, 2 x, 5 x, \ldots \] A. -3 B. \( -3 x \) C. 3 D. \( 3 x \) Option 1 Option 2 Option 3 Option 4 Submit Clear form Never submit passwords through Google Forms. This form was created inside of NYC Department of Education. Does this form look suspicious? Report ! Google Forms
Ask by Munoz Joseph. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The common difference is \( 3x \).
Solution
1. The sequence given is
\[
-7x,\: -4x,\: -x,\: 2x,\: 5x,\ldots
\]
2. The common difference \( d \) in an arithmetic sequence is defined as the difference between any term and its preceding term.
3. Calculate the common difference using the first two terms:
\[
d = (-4x) - (-7x) = -4x + 7x = 3x.
\]
4. Hence, the common difference of the sequence is
\[
3x.
\]
5. The correct answer is Option D: \( 3x \).
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Simplify this solution Bonus Knowledge
The common difference in an arithmetic sequence is found by subtracting the first term from the second term (or any subsequent terms). In the sequence given, you can simply compute the difference by taking \(-4x - (-7x)\). This equates to \(-4x + 7x\), which simplifies to \(3x\). So, the common difference is \(3x\). This common difference is critical for determining any term in the sequence and helps in understanding how the sequence evolves. For example, if you need to find the 10th term, you'd use the initial term and add \(9\) times the common difference to it! So, it’s not just a number—it's a key to unlocking patterns in arithmetic sequences!
