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 \( d=3 \). (Type a whole number.) (b) Find the eighth term. The eighth term is \( a_{8}=27 \). (Type a whole number.) (c) Find a recursive rule for the nth term. \( \square \) (Type an equation.)

The recursive rule for the nth term of the arithmetic sequence can be expressed as: \( a_n = a_{n-1} + 3 \) with \( a_1 = 6 \). This means that to get to the next term, you simply add the common difference of 3 to the previous term! For those who enjoy patterns, did you know that arithmetic sequences can be seen in many daily situations? Think of it like climbing stairs—each step up is like adding the common difference, allowing us to reach new heights term by term. This progression can help in understanding everything from finance to time management!