# What is the 30th term of the arithmetic series 2, 5, 8, … ?

Nov 14, 2015

$89$

#### Explanation:

One way to tackle this would be to count up all the way to the 30th term.

The more elegant way would be to create a linear equation, where $f \left(x\right)$ is the number in the sequence and $x$ is the term number.

We can see that the arithmetic sequence rises by $3$ each term, so $3$ is our slope. We also know that the first term is $2$ (when $x = 1$), so we can figure out that our equation must be $f \left(x\right) = 3 x - 1$.

With this, we can plug in $30$ for $x$ and get $\textcolor{red}{89}$.