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

Oct 3, 2016

${u}_{r} = 3 r + 2$
${u}_{r} = {u}_{\text{r-1}} + 3$ 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...
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.