Question

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

A(n) = –6 + (n – 1)(6)


–6, 18, 54


–6, 12, 48


0, 18, 54


6, 18, 54

Answer 1

To find the first, fourth, and tenth terms of the arithmetic sequence described by the rule \( A(n) = -6 + (n - 1)(6) \), we can calculate them as follows:

1. **First term \( A(1) \)**:
\[
A(1) = -6 + (1 - 1)(6) = -6 + 0 = -6
\]

2. **Fourth term \( A(4) \)**:
\[
A(4) = -6 + (4 - 1)(6) = -6 + 3(6) = -6 + 18 = 12
\]

3. **Tenth term \( A(10) \)**:
\[
A(10) = -6 + (10 - 1)(6) = -6 + 9(6) = -6 + 54 = 48
\]

Now, we have the first, fourth, and tenth terms:
- First term: \(-6\)
- Fourth term: \(12\)
- Tenth term: \(48\)

Thus, the answer is:
\(-6, 12, 48\)