Question

Hello, I need help writing a recursive formula for these I’m struggling bad

Answer 1

1) Notice that:

`\begin{gathered} 3=(30)/(10), \\ (3)/(10)=(3)/(10), \\ (3)/(100)=((3)/(10))/(10). \end{gathered}`

Therefore the recursive formula for the first sequence is:

`\begin{gathered} a_1=30, \\ a_n=(a_(n-1))/(10)\text{ for }n\geq2. \end{gathered}`

2) Notice that:

`\begin{gathered} 11=14-3, \\ 8=11-3, \\ 5=11-3. \end{gathered}`

Therefore the recursive formula for the second sequence is:

`\begin{gathered} a_1=14, \\ a_n=a_(n-1)-3\text{ for }n\geq2. \end{gathered}`

Answer:

Left sequence:

`\begin{gathered} a_1=30, \\ a_n=(a_(n-1))/(10)\text{ for }n\geq2. \end{gathered}`

Right sequence:

`\begin{gathered} a_1=14, \\ a_n=a_(n-1)-3\text{ for }n\geq2. \end{gathered}`