# How do you find the explicit formula for the following sequence 2, 4, 6, 8,...?

Nov 23, 2017

${a}_{n} = {a}_{1} + 2 \left(n - 1\right) = 2 + 2 \left(n - 1\right)$

#### Explanation:

Each term is 2 greater than the term before it. Thus for any given term, ${a}_{n}$, our equation is:

${a}_{n} = 2 n$

We can write this in a form closer to standard, by noting that ${a}_{1} = 2$, so we can make it dependent on ${a}_{1}$..

${a}_{n} = {a}_{1} + 2 \left(n - 1\right) = 2 + 2 \left(n - 1\right)$