Answer :
To find the [tex]\(8^{\text{th}}\)[/tex] term of the sequence, we need to understand how arithmetic sequences work. An arithmetic sequence has a pattern where each term is a fixed amount more than the previous term. This fixed amount is called the common difference.
For the given sequence:
1. The first term is [tex]\(f(1) = 4\)[/tex].
2. The common difference is [tex]\(7\)[/tex].
To find any term in an arithmetic sequence, you can use the formula for the [tex]\(n^{\text{th}}\)[/tex] term:
[tex]\[
f(n) = f(1) + (n - 1) \times \text{common difference}
\][/tex]
In this problem, we need to find the [tex]\(8^{\text{th}}\)[/tex] term ([tex]\(f(8)\)[/tex]). Let's plug the values into the formula:
- The first term, [tex]\(f(1)\)[/tex], is 4.
- The common difference is 7.
- We want the [tex]\(8^{\text{th}}\)[/tex] term, so [tex]\(n = 8\)[/tex].
Use the formula:
[tex]\[
f(8) = 4 + (8 - 1) \times 7
\][/tex]
Calculating this step-by-step:
- Calculate [tex]\(8 - 1\)[/tex], which is 7.
- Multiply 7 by the common difference, which is 7, so [tex]\(7 \times 7 = 49\)[/tex].
- Add this result to the first term: [tex]\(4 + 49 = 53\)[/tex].
Therefore, the [tex]\(8^{\text{th}}\)[/tex] term of the sequence is [tex]\(53\)[/tex].
The correct option is D. 53.
For the given sequence:
1. The first term is [tex]\(f(1) = 4\)[/tex].
2. The common difference is [tex]\(7\)[/tex].
To find any term in an arithmetic sequence, you can use the formula for the [tex]\(n^{\text{th}}\)[/tex] term:
[tex]\[
f(n) = f(1) + (n - 1) \times \text{common difference}
\][/tex]
In this problem, we need to find the [tex]\(8^{\text{th}}\)[/tex] term ([tex]\(f(8)\)[/tex]). Let's plug the values into the formula:
- The first term, [tex]\(f(1)\)[/tex], is 4.
- The common difference is 7.
- We want the [tex]\(8^{\text{th}}\)[/tex] term, so [tex]\(n = 8\)[/tex].
Use the formula:
[tex]\[
f(8) = 4 + (8 - 1) \times 7
\][/tex]
Calculating this step-by-step:
- Calculate [tex]\(8 - 1\)[/tex], which is 7.
- Multiply 7 by the common difference, which is 7, so [tex]\(7 \times 7 = 49\)[/tex].
- Add this result to the first term: [tex]\(4 + 49 = 53\)[/tex].
Therefore, the [tex]\(8^{\text{th}}\)[/tex] term of the sequence is [tex]\(53\)[/tex].
The correct option is D. 53.