Question

How do you write both an explicit equation and a recursive equation for the sequence: `5,8, 11, 14, 17,...`?

Answer 1

`u_r=3r+2`
`u_r=u_"r-1"+3` where `u_1=5`

Explanation:

The sequence goes up in 3s. The sequence we are really familiar with is the 3times table ....3,6,9,12 etc
3x1, 3x2, 3x3...
This sequence just needs adjusting by adding 2 to each term.
3x1+2, 3x2+2, 3x3+2 etc 3r+2

Or for the recurrence relationship we look at how we get from one term to the next. In this case add 3 each time. And of course we need to state which the first term is.