7.

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

A(n) = –6 + (n – 1)(6)

1 answer

To find the first, fourth, and tenth terms of the arithmetic sequence described by the rule \( A(n) = -6 + (n - 1)(6) \), we can substitute the respective values of \( n \) into the formula.

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

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

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

Thus, the first term is \(-6\), the fourth term is \(12\), and the tenth term is \(48\).

Summary of results:

  • First term: \(-6\)
  • Fourth term: \(12\)
  • Tenth term: \(48\)