The sequence beginning with 3, 7... follows this rule:

So since 7 is the second term, we multiply 2 by 4 and add it to 7. We get 15

Our sequence so far: 3,7,15,

Then we multiply 4 and 4 to get 16 as 15 is the FOURTH term then add 16 to 15. We get 31.

Do you notice a pattern? 3,7,15,31.

Yes 2n+1 can represent each change for the terms.

So we keep calculating...

A little confusing, but....

Term  number   1   2    3     4     5      6     7

                          3  7   15    27   43   63   87

Note that the 3rd term  = previous term + 4 times the previous term number  = 7 + 4(2) = 15

4th term  =  15 + 4(3)  = 27

5th term = 27 + 4(4)  = 43

6th term =  43 + 4(5) = 63

7th term = 63 + 4(6) = 87

Notice something else.....the difference between terms is   4, 8, 12, 16, 20, 24

Just for the heck of it, what would be the 8th term   ????