Use the functional relations below to write the first five terms.

1. A(n)= 3n² + 1

To find the first five terms of the sequence \( A(n) = 3n^2 + 1 \), we simply substitute \( n \) with the first five positive integers (i.e., \( n = 1, 2, 3, 4, 5 \)) and calculate the corresponding values.

1. For \( n = 1 \):
   \[
   A(1) = 3(1)^2 + 1 = 3 \cdot 1 + 1 = 4
   \]

2. For \( n = 2 \):
   \[
   A(2) = 3(2)^2 + 1 = 3 \cdot 4 + 1 = 12 + 1 = 13
   \]

3. For \( n = 3 \):
   \[
   A(3) = 3(3)^2 + 1 = 3 \cdot 9 + 1 = 27 + 1 = 28
   \]

4. For \( n = 4 \):
   \[
   A(4) = 3(4)^2 + 1 = 3 \cdot 16 + 1 = 48 + 1 = 49
   \]

5. For \( n = 5 \):
   \[
   A(5) = 3(5)^2 + 1 = 3 \cdot 25 + 1 = 75 + 1 = 76
   \]

Thus, the first five terms of the sequence \( A(n) = 3n^2 + 1 \) are:

1. \( A(1) = 4 \)
2. \( A(2) = 13 \)
3. \( A(3) = 28 \)
4. \( A(4) = 49 \)
5. \( A(5) = 76 \)

Would you like further details or have any questions?

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### Related Questions

1. What is the 10th term of the sequence \( A(n) = 3n^2 + 1 \)?
2. How would the sequence change if the formula were \( A(n) = 3n^2 - 1 \)?
3. Can you find a general term for a sequence that is similar but includes a linear term, such as \( A(n) = 3n^2 + 2n + 1 \)?
4. What is the sum of the first five terms of the sequence \( A(n) = 3n^2 + 1 \)?
5. How does the growth of this quadratic sequence compare to an arithmetic sequence with a common difference of 5?
6. Can you find the 100th term of the sequence \( A(n) = 3n^2 + 1 \)?
7. How would you graph the first five terms of \( A(n) = 3n^2 + 1 \)?
8. What is the second difference of the sequence \( A(n) = 3n^2 + 1 \)?

### Tip

To identify the type of sequence, look at the highest power of \( n \) in the formula: if it is \( n^2 \), the sequence is quadratic; if it is \( n \), the sequence is linear.

Explore how to calculate the first five terms of the sequence A(n) = 3n^2 + 1 with detailed step-by-step solutions. This problem involves quadratic sequences and covers calculating sequence terms using a given formula. Suitable for Grades 9-12 students.

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