Question

Write a recursive sequence that represents the sequence defined by the following explicit formula: an= 8 - 5(n - 1)

Answer 1

The explicit formula of the arithmetic sequence is:

`a_n=a_1+(n-1)d`

Given the formula

`a_n=8-5(n-1)`

then,

a1 = 8

d = -5

The recursive formula of the arithmetic sequence is:

`\begin{cases}a_1 \\ a_n=a_(n-1)+d\end{cases}`

In this case:

`\begin{cases}a_1=8 \\ a_n=a_(n-1)-5\end{cases}`