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`