Writing a Recursive Formula for an Arithmetic Sequence

Write a recursive formula for the arithmetic sequence.

{- 18, - 7, 4, 15, 26, …}

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 first term is given as $−18$ . The common difference can be found by subtracting the first term from the second term.
$d = −7 - (−18) = 11$
Substitute the initial term and the common difference into the recursive formula for arithmetic sequences.
$\begin{array}{l} a_{1} = - 18 \\ a_{n} = a_{n - 1} + 11, for n \geq 2 \end{array}$

Your turn

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

Write a recursive formula for the arithmetic sequence.

{25, 37, 49, 61, …}

How did it go?