Question

Write a recursion formula for the sequence. 5, 14, 23, 32, …Choose the correct formula below:

Answer 1

Given

Write a recursion formula for the sequence.

5, 14, 23, 32, …

`\begin{gathered} \text{The co}mmondifference=a_2-a_1 \\ \text{The co}mmon\text{ difference =14-5} \\ \text{The co}mmon\text{ difference =9} \end{gathered}`

Formula

`\begin{gathered} a_n=a_1+(n-1)d \\ \\ a_1=5 \\ d=9 \\ a_n=5+(n-1)9 \\ a_n=5+(9n-9) \\ \\ a_n=5+9n-9 \\ a_n=9n-9+5 \\ a_n=9n-4 \end{gathered}`

Option C is correct

`\begin{gathered} a_n=a_(n-1)+9 \\ \text{when n=2} \\ a_2=a_(2-1)+9 \\ a_2=a_1+9 \\ a_2=5_{}+9 \\ a_2=14 \end{gathered}`