Question

Consider the sequence:

3, 8, 13, 18, 23, ....

The recursive formula for this sequence is:

LaTeX: a_n=a_{n-1}+5a n = a n − 1 + 5.

In complete sentences, explain what LaTeX: a_na n, LaTeX: a_{n-1}a n − 1, and the 5 represent in the formula. Find LaTeX: a_8a 8. What do you need to know in order to find LaTeX: a_8a 8?

Answer 1

Yep

Explanation:

Answer 2

The recursive formula

`a_n=a_(n-1)+5`

means that the current element (
`a_n`) is written in terms of the term immediately before (
`a_(n-1)`).

In order to get
`a_n`, you have to add 5 to the previous term
`a_(n-1)`. In other words, every term is 5 more than its predecessor.

So, if we want the 8th term, we can keep adding 5 until we get there:

`\begin{array}cn&a_n\\1&3\\2&8\\3&13\\4&18\\5&23\\6&28\\7&33\\8&38\end{array}`