Find the nth term of the sequence 3,7,11,15...

We are searching for a rule that when we put in n (n represetning where the term is in the sequence eg. 3 is the first term so n will be 1) our output is the sequence above. This rule will most likely be in the form an+b. Let's begin by finding a. a can be found by calculating the steps that the sequence makes from term to term, in this case 4. This means that each input n is being multiplied by 4 to reach to output. However now if we put in 1 to 4n we have an output of 4 not 3. How do we get from 4 to 3 or 8 (2x4) to 7? -1. Therefore our b must be -1 to make our rule true for the sequence we have been given. Our nth term is therefore 4n-1.