# How do you find the explicit formula for the following sequence 4 + 7 + 10 ... +67?

Feb 29, 2016

3n + 1

#### Explanation:

For an $\textcolor{b l u e}{\text{ Arithmetic sequence }}$

a , a + d , a +2d , a + 3d , .........................., a+(n-1)d

the nth term is a + (n - 1 )d

here a = 4 and d = 7 - 4 = 10 - 7 = 3

$\Rightarrow \text{ formula is } : 4 + 3 \left(n - 1\right) = 4 + 3 n - 3 = 3 n + 1$