Writing the nth Term Explicit Formula for an Arithmetic Sequence

Write an explicit formula for the arithmetic sequence.

{2, 12, 22, 32, 42, …}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The common difference can be found by subtracting the first term from the second term.
$\begin{array}{l} d & = a_{2} - a_{1} \\ = 12 - 2 \\ = 10 \end{array}$
The common difference is 10. Substitute the common difference and the first term of the sequence into the formula and simplify.
$\begin{array}{l} a_{n} = 2 + 10 (n - 1) \\ a_{n} = 10 n - 8 \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write an explicit formula for the following arithmetic sequence.

{50, 47, 44, 41, \dots}

How did it go?