Exercise 1 Page 575

To begin, let's observe the given terms in the sequence to determine the value of the first term as well as the common difference. We can use this information to write an equation for the $n\text{th}$ term of the sequence.

Writing the Equation

Explicit equations for the $n\text{th}$ term of an arithmetic sequence follow a certain format. In this form, $a_1$ is the first term in the sequence, $d$ is the common difference, and $n$ is the position of the desired term in the sequence. Using the common difference $d=6$ and the first term $a_1=2,$ we can write and simplify the equation.

Solving for the $n\text{th}$ Term

To find the value of the $10\text{th}$ term, we substitute $n=10$ into this equation and simplify. The $10\text{th}$ term in the sequence is $56.$