Question

Write a recursive formula for the arithmetic sequence:a={12,17,22,...}a_1=Answera_n = a_{n-1} + Answer

Answer 1

$\begin{gathered} a_{1}=\textbf{12} \\ a_{n}=a_{n-1}+\textbf{5n} \end{gathered}$

1) A Recursive formula refers always to the previous term.

2) In this Arithmetic Sequence, the common difference is 5, the first term is 12. So we can set the following Arithmetic Sequence:

$\begin{gathered} a_{1}=\textbf{12} \\ a_2=12+5n \\ a_n=a_{n-1}+\textbf{5n} \end{gathered}$

Thus, this is the answer.