# If a_0=7 and a_(n+1)=a_n+12 for n>=0, how do you find the values of a_5?

Jan 7, 2017

${a}_{5} = 55$

#### Explanation:

This recursive definition describes an arithmetic sequence with initial term $7$ and common difference $12$.

The general term of an arithmetic sequence can be written:

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

where $a$ is the initial term and $d$ the common difference.

So in our example, $a = 7$, $d = 12$ and:

${a}_{5} = a + d \left(5 - 1\right) = a + 4 d = 7 + 4 \cdot 12 = 7 + 48 = 55$