The sequence below is arithmetic. Complete parts (a) through (d) below. \( 6,9,12,15, \ldots \) (a) Find the common difference. The common difference is \( \mathrm{d}=3 \). (Type a whole number.) (b) Find the eighth term. The eighth term is \( \mathrm{a}_{8}=27 \). (Type a whole number.) (c) Find a recursive rule for the nth term. \( \mathrm{a}_{\mathrm{n}}=\mathrm{a}_{\mathrm{n}}-1+3 \) (Type an equation.) (d) Find an explicit rule for the nth term. \( \square \) (Type an equation.) Get more help \& (Tlear all

Sure, let's complete part **(d)** of the problem. ### (d) Find an explicit rule for the nth term. An **explicit rule** for an arithmetic sequence allows you to find the \( n \)th term directly without needing to reference the previous term. The general form of the explicit rule for an arithmetic sequence is: \[ a_n = a_1 + (n - 1) \times d \] Where: - \( a_n \) is the \( n \)th term. - \( a_1 \) is the first term. - \( d \) is the common difference. - \( n \) is the term number. Given the sequence: \( 6, 9, 12, 15, \ldots \) - \( a_1 = 6 \) - \( d = 3 \) (from part a) Plugging these values into the formula: \[ a_n = 6 + (n - 1) \times 3 \] Simplify the equation: \[ a_n = 6 + 3n - 3 \] \[ a_n = 3n + 3 \] **Therefore, the explicit rule for the nth term is:** \[ a_n = 3n + 3 \]