Question

Write a recursive sequence that represents the sequence defined by the followingexplicit formula

Answer 1

Substituting n=1 in the given formula we get:

`a_1=-5+3(1+1)=-5+3\cdot2=-5+6=1.`

Also, notice that:

`\begin{gathered} a_n=-5+3(n+1)=-5+3(n-1+1+1)=-5+3((n-1)+1)+3 \\ =a_(n-1)+3. \end{gathered}`

Answer:

`\begin{gathered} a_1=1, \\ a_n=a_(n-1)+3. \end{gathered}`