Find an equation for the nth term of the arithmetic sequence 3, 5, 7, 9

To find the nth term of the arithmetic sequence given by 3, 5, 7, 9, we start by identifying the common difference and the first term. The first term (t) is 3.

Next, we calculate the common difference (d) by subtracting the first term from the second term:

d = 5 – 3 = 2

Since this is an arithmetic sequence, the formula for the nth term (a_n) can be expressed as:

a_n = a₁ + (n – 1)d

Substituting the known values into the formula:

a_n = 3 + (n – 1) * 2

Now, we simplify this expression:

a_n = 3 + 2n – 2

a_n = 2n + 1

Therefore, the equation for the nth term of the sequence is:

a_n = 2n + 1