Question
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
5, , mc017-3.jpg
5, , mc017-9.jpg
6, , mc017-5.jpg
0, , mc017-7.jpg
5, , mc017-3.jpg
5, , mc017-9.jpg
6, , mc017-5.jpg
0, , mc017-7.jpg
Answers
Answered by
GPT-4o mini
To find the first, fourth, and tenth terms of the arithmetic sequence, we first need to identify the pattern in the sequence.
The given sequence appears to start with the number 5 and may continue with a consistent addition (common difference). However, the common difference is not explicitly provided in the question.
For arithmetic sequences, the nth term can be calculated as:
\[ a_n = a_1 + (n - 1)d \]
Where:
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( n \) is the term number,
- \( d \) is the common difference.
Assuming your incomplete sequence starts as follows:
1. **First Term (a_1)**:
- \( a_1 = 5 \)
To compute the fourth and tenth terms, we need the common difference \( d \). However, we can proceed to calculate the fourth and tenth terms by assuming a common difference. Let's assume \( d = x \).
2. **Fourth Term (a_4)**:
\[
a_4 = a_1 + (4 - 1)d = 5 + 3d
\]
3. **Tenth Term (a_{10})**:
\[
a_{10} = a_1 + (10 - 1)d = 5 + 9d
\]
If you can provide the actual common difference, we can extract precise values.
However, based on the options you've provided, I'll clarify the structure for finding terms:
Assuming it was fully provided, we could fill in the gaps at the known intervals. If let's just assume \( d = 1 \) for a simple case:
1. **First term**: 5
2. **Fourth term**: 5 + 3(1) = 8
3. **Tenth term**: 5 + 9(1) = 14
If you provide the common difference, I can provide the correct fourth and tenth terms. For example, if you confirm the common difference, we can generate statements like:
- For common difference of 1: \( 5, 6, 7, 8, 9, 10 \) gives \( a_4 = 8 \), \( a_{10} = 14 \).
- If common difference is different like 2, then you'd adjust accordingly.
Please provide the necessary details or clarify the sequence further for exact answers.
The given sequence appears to start with the number 5 and may continue with a consistent addition (common difference). However, the common difference is not explicitly provided in the question.
For arithmetic sequences, the nth term can be calculated as:
\[ a_n = a_1 + (n - 1)d \]
Where:
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( n \) is the term number,
- \( d \) is the common difference.
Assuming your incomplete sequence starts as follows:
1. **First Term (a_1)**:
- \( a_1 = 5 \)
To compute the fourth and tenth terms, we need the common difference \( d \). However, we can proceed to calculate the fourth and tenth terms by assuming a common difference. Let's assume \( d = x \).
2. **Fourth Term (a_4)**:
\[
a_4 = a_1 + (4 - 1)d = 5 + 3d
\]
3. **Tenth Term (a_{10})**:
\[
a_{10} = a_1 + (10 - 1)d = 5 + 9d
\]
If you can provide the actual common difference, we can extract precise values.
However, based on the options you've provided, I'll clarify the structure for finding terms:
Assuming it was fully provided, we could fill in the gaps at the known intervals. If let's just assume \( d = 1 \) for a simple case:
1. **First term**: 5
2. **Fourth term**: 5 + 3(1) = 8
3. **Tenth term**: 5 + 9(1) = 14
If you provide the common difference, I can provide the correct fourth and tenth terms. For example, if you confirm the common difference, we can generate statements like:
- For common difference of 1: \( 5, 6, 7, 8, 9, 10 \) gives \( a_4 = 8 \), \( a_{10} = 14 \).
- If common difference is different like 2, then you'd adjust accordingly.
Please provide the necessary details or clarify the sequence further for exact answers.