Question

Write an explicit formula that represents the sequence defined by the following recursive formula: a1=-1 and an =an-1+7

Answer 1

We have the following:

$\begin{gathered} a_1=-1 \\ a_n=a_{n-1}+7 \end{gathered}$

now,

$\begin{gathered} a_n=a_{n-1}+d\rightarrow d=7 \\ n=1\rightarrow a_1=a_{1-1}+d\rightarrow a_1=a_0+7 \\ -1=a_0+7 \\ a_0=-1-7 \\ a_0=-8 \end{gathered}$

Therefore:

$\begin{gathered} a_n=a_1+d(n-1)_{} \\ a_n=-1+7(n-1) \\ a_n=-1+7n-7 \\ a_n=7n-8 \end{gathered}$

The explicit formula:

$a_n=7n-8$