Find a formula for an for the arithmetic sequence.4, -5, -14, -23, -32,. . .

The given sequence is an arithmetic sequence. In an arithmetic sequence, the difference between any two successive terms is constant. This difference is also known as the common difference.

Step 1: Find the common difference The common difference (d) can be found by subtracting the first term from the second term. In this case, -5 - 4 = -9.

Step 2: Write the formula The formula for an arithmetic sequence is:

a_n = a_1 + (n - 1) * d

where: a_n is the nth term of the sequence, a_1 is the first term of the sequence, d is the common difference, and n is the term number.

Step 3: Substitute the values into the formula So, for this sequence, the formula becomes:

a_n = 4 + (n - 1) * -9

This is the formula for the given arithmetic sequence.