Question

3, 8, 13, 18, 23, 28, 33, 38

What is the recursive function?
What is the explicit function?

I don't completely understand the two functions, if anyone could help me out that would be great :)

Answer 1

The given series is

$3,8,13,18,23,28,33,38,...$

Where the first term, a , is 3.

And the difference is constant, that is

$8-3=13-8=18-13=5$

So the constant difference, d is 3.

Since the difference is constant, so the given series is arthmetic.

And for explicit rule, we use the formula of nth term, which is

$a_{n}= a+(n-1)d$

Substituting the values of a and d, we will get

$a_{n} = 3+(n-1)5 \\ a_{n} = 3+5n-5 \\ a_{n} = 5n -2$

Recursive rule is used to tell us the relationship between previous and current term. And the required rule is

$a_{n} = a_{n-1} +5 , a_{1} = 3$