Find a formula for the nth term of the arithmetic sequence 32, 36, 40, 44

To find the formula for the nth term of the given arithmetic sequence, we first need to identify the first term and the common difference.

The first term of the sequence (a₁) is 32. Next, to find the common difference (d), we subtract the first term from the second term:

d = 36 – 32 = 4

Now, we can use the formula for the nth term of an arithmetic sequence, which is:

a_n = a₁ + (n – 1)d

Substituting the values we found:

a_n = 32 + (n – 1) * 4

Simplifying this further gives:

a_n = 32 + 4n – 4

a_n = 4n + 28

So, the formula for the nth term of the arithmetic sequence is:

a_n = 4n + 28

This formula allows you to find any term in the sequence by simply substituting the value of n.