# An arithmetic sequence is given by 5, 8, 11,... How do you find the value of d?

Jul 18, 2018

$\textcolor{b l u e}{d = 3}$

#### Explanation:

The nth term of an arithmetic sequence is given by:

$a + \left(n - 1\right) d$

Where $\boldsymbol{a}$ is the first term, $\boldsymbol{d}$ is the common difference and $\boldsymbol{n}$ is the nth term.

We have:

$a = 5$

looking at the second element, we have:

$5 + \left(2 - 1\right) d = 8$

$5 + d = 8 \implies d = 3$

Jul 18, 2018

$d = 3$

#### Explanation:

In an arithmetic sequence, $d$ is our common difference, or the value we add/subtract to go to the next term.

To get from $5$ to $8$, we can add $3$.

To get from $8$ to $11$, we can add $3$.

In an arithmetic sequence, we always add or subtract the same amount. We see that to get to the next term, we add $3$.

This is our $d$.

Hope this helps!