Question

Write an expression for the \(n\) th term of the sequence. (There is more than one correct answer.) \(3,7,11,15, \ldots\)

Short answer

The expression for the n-th term of the sequence is \(a_n = -1 + 4n\).

Step-by-step solution

Find the common difference

The common difference can be found by subtracting any term from the previous term. Here, subtracting the first term (3) from the second term (7) gives us a common difference (d) of 4.

Formulate the sequence expression

We can formulate the general expression for arithmetic sequence, which is \(a_n = a_1 + (n-1)*d\). Here, \(a_1\) is the first term of the sequence, and \(d\) is the common difference. Substituting these values into the formula gives us the n-th term expression: \(a_n = 3 + (n-1)*4.\)

Simplify the sequence expression

We can simplify this expression further by distributing the 4 in the equation. The simplified expression will look like this: \(a_n = -1 + 4n\).