The nth Term of a Linear Sequence

Instead of adding the common difference over and over, you can write a formula that gives you any term directly. For a linear sequence the nth term rule always looks like

where $d$ is the common difference and $c$ is a constant you work out. To find $c$, compare the first term of the sequence to $d \times 1$.

For example, the sequence $5,; 8,; 11,; 14,; \\$ has a common difference of $3$. The multiples of 3 are $3,; 6,; 9,; 12,; \\$ Each term in the sequence is 2 more than the corresponding multiple of 3, so the nth term is $3n + 2$.

Adjust the common difference and zero term sliders until the line passes through every dot. The common difference is the gradient; the zero term is where the line starts.

Watch it work

Question: Find the nth term of $4,; 7,; 10,; 13,; \\$

Have a go