To find the sum of the 1st and 5th terms of the sequence represented by the function $a(n) = 3n - 7$, we need to calculate the values of $a(1)$ and $a(5)$, and then sum them.

Step 1: Calculate the 1st term $a(1)$

Substitute $n = 1$ into the function: $a(1) = 3(1) - 7 = 3 - 7 = -4$

Step 2: Calculate the 5th term $a(5)$

Substitute $n = 5$ into the function: $a(5) = 3(5) - 7 = 15 - 7 = 8$

Step 3: Find the sum of the 1st and 5th terms

Now, add $a(1)$ and $a(5)$: $\text{Sum} = a(1) + a(5) = -4 + 8 = 4$

Final Answer:

The sum of the 1st and 5th terms is $\boxed{4}$.

Would you like more details or have any further questions on this? Here are 5 related questions to explore:

1. How do you calculate the sum of terms in an arithmetic sequence?
2. What is the general formula for the $n$-th term in an arithmetic sequence?
3. How would the sum change if the formula was $a(n) = 5n - 7$?
4. How can you calculate the 10th term of the sequence $a(n) = 3n - 7$?
5. What is the significance of the formula in real-life applications, like business or science?

Tip: In sequences, each term depends on the previous term or a specific formula, and arithmetic sequences have a consistent difference between successive terms.