Answer :
- Substitute $n=8$ into the function $f(n) = 7n - 3$.
- Calculate $7 Imes 8 = 56$.
- Subtract 3 from 56: $56 - 3 = 53$.
- The $8^{\text{th}}$ term of the sequence is $\boxed{53}$.
### Explanation
1. Understanding the Problem
We are given the function of an arithmetic sequence $f(n) = 7n - 3$, and we want to find the $8^{\text{th}}$ term of the sequence. This means we need to find the value of $f(8)$.
2. Substituting n=8
To find the $8^{\text{th}}$ term, we substitute $n = 8$ into the function:$$f(8) = 7(8) - 3$$
3. Calculating f(8)
Now, we perform the calculation:$$f(8) = 56 - 3 = 53$$
4. Final Answer
Therefore, the $8^{\text{th}}$ term of the sequence is 53.
### Examples
Arithmetic sequences are useful in many real-life situations, such as calculating the cost of items with a fixed increase, predicting the number of seats in rows of a theater, or determining the height of stacked objects. For example, if you save $7 each week but start with a debt of $3, the formula f(n) = 7n - 3 describes your savings after n weeks. Finding the 8th term tells you how much you've saved after 8 weeks.
- Calculate $7 Imes 8 = 56$.
- Subtract 3 from 56: $56 - 3 = 53$.
- The $8^{\text{th}}$ term of the sequence is $\boxed{53}$.
### Explanation
1. Understanding the Problem
We are given the function of an arithmetic sequence $f(n) = 7n - 3$, and we want to find the $8^{\text{th}}$ term of the sequence. This means we need to find the value of $f(8)$.
2. Substituting n=8
To find the $8^{\text{th}}$ term, we substitute $n = 8$ into the function:$$f(8) = 7(8) - 3$$
3. Calculating f(8)
Now, we perform the calculation:$$f(8) = 56 - 3 = 53$$
4. Final Answer
Therefore, the $8^{\text{th}}$ term of the sequence is 53.
### Examples
Arithmetic sequences are useful in many real-life situations, such as calculating the cost of items with a fixed increase, predicting the number of seats in rows of a theater, or determining the height of stacked objects. For example, if you save $7 each week but start with a debt of $3, the formula f(n) = 7n - 3 describes your savings after n weeks. Finding the 8th term tells you how much you've saved after 8 weeks.
