# How to make a formula to link two sequences without any positioning numbers?

I have two sequences:

sequence $n$: $4, 7, 10, 13$

sequence $p: 10, 16, 22, 28$

I wish to find a link between them i.e. $p=??$

However, I cannot use positioning numbers, so you can't say that $4$ is the first term, $7$ is the second term, etc.

Is this possible?

Thank you

• Am I totally confusing myself...? – Turbo Apr 18 '14 at 19:09
• Not sure what you mean. Something like $p=2n+2$? – Hagen von Eitzen Apr 18 '14 at 19:11
• @HagenvonEitzen That's right and obvious, but what are the steps to find the formula? – Turbo Apr 18 '14 at 19:23

By observing, guessing and then verifying, we see that the sequences are related by $p=2n+2$.

• Yes, it's simple, but what are the actual steps to find the formula? – Turbo Apr 18 '14 at 19:23
• I observe, guess and verify that you are right! – Turbo Apr 18 '14 at 19:25
• Why not include that in your answer and I'll choose it as the right answer? ;) – Turbo Apr 18 '14 at 19:25