# How do you find the explicit formula for the following sequence 5, 8, 11, 14, . . .?

Feb 20, 2016

An explicit formula of an arithmetic series includes all given information.

#### Explanation:

${t}_{n} = a + \left(n - 1\right) d$

${t}_{n} = 5 + \left(n - 1\right) 3$

${t}_{n} = 2 + 3 n$

As you can see, we don't know the number of terms, so we leave it as n. We can find ${t}_{n}$ with this formula by plugging in ${t}_{n}$ or n.

Hopefully this helps!