Question

Question shown in picture below!!(i only need the 2nd one)

Answer 1

Given the following sequence:

`\mleft\lbrace17,14,11,8,\ldots\mright\rbrace`

notice that the common difference between each term is -3, therefore, we can use the explicit formula for a sequence:

`\begin{gathered} a_n=a_1+(n-1)\cdot d \\ d=-3 \\ a_1=17 \\ \Rightarrow a_n=17+(n-1)(-3) \\ \Rightarrow a_n=17-3n+3=20-3n \\ a_n=20-3n \end{gathered}`

we have that the explicit formula is a_n=20-3n, while the recursive formula is:

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