Answer :
To find the 8th term of the arithmetic sequence given by the function [tex]\( f(n) = 7n - 3 \)[/tex], we need to evaluate this function at [tex]\( n = 8 \)[/tex]. Here's how you can do it step-by-step:
1. Understand the function: The function [tex]\( f(n) = 7n - 3 \)[/tex] represents an arithmetic sequence where:
- The first term is determined by substituting [tex]\( n = 1 \)[/tex] into the function, i.e., [tex]\( f(1) = 7 \times 1 - 3 = 4 \)[/tex].
- The common difference can be deduced from the formula, as the coefficient of [tex]\( n \)[/tex], which is 7.
2. Calculate the 8th term: To find the 8th term, substitute [tex]\( n = 8 \)[/tex] into the function:
[tex]\[
f(8) = 7 \times 8 - 3
\][/tex]
3. Perform the calculation:
[tex]\[
7 \times 8 = 56
\][/tex]
[tex]\[
56 - 3 = 53
\][/tex]
4. Conclusion: The 8th term of the sequence is 53.
Therefore, the correct answer is [tex]\( \boxed{53} \)[/tex], which corresponds to option C.
1. Understand the function: The function [tex]\( f(n) = 7n - 3 \)[/tex] represents an arithmetic sequence where:
- The first term is determined by substituting [tex]\( n = 1 \)[/tex] into the function, i.e., [tex]\( f(1) = 7 \times 1 - 3 = 4 \)[/tex].
- The common difference can be deduced from the formula, as the coefficient of [tex]\( n \)[/tex], which is 7.
2. Calculate the 8th term: To find the 8th term, substitute [tex]\( n = 8 \)[/tex] into the function:
[tex]\[
f(8) = 7 \times 8 - 3
\][/tex]
3. Perform the calculation:
[tex]\[
7 \times 8 = 56
\][/tex]
[tex]\[
56 - 3 = 53
\][/tex]
4. Conclusion: The 8th term of the sequence is 53.
Therefore, the correct answer is [tex]\( \boxed{53} \)[/tex], which corresponds to option C.