2, 7, 26, 101, 400, ?

It's not a geometric sequence, but it goes up fast like 
one, so let's see how close it is to one.

The ratios of each term to the preceding one are
7/2 = 3.5
26/7 = 3.714
101/26 = 3.885
400/101 = 3.960

Those ratios seem to be getting close to 4.
So let's investigate how close each term is to 
being 4 times the preceding term

Term #1:  7 is close to 4×2 which is 8.  It's just 1 less.
Term #2:  26 is close to 4×7 which is 28.  It's just 2 less.
Term #3:  101 is close to 4×26 which is 104.  It's just 3 less.
Term #4:  400 is close to 4×101 which is 404.  It's just 4 less.

Aha.  Now we see the pattern.

Each term is 4 times the preceding term minus the number of term.

So term #5 will be 4×400 = 1600. Then 1600-5 (the term number) = 1595

-----------------------------------------

7, 21, 8, 72, 9

It looks like the odd terms have the pattern 7,8,9,10,11,...
Term #1 is 7
Term #2 is 21 or 7×31, and 1 is half of 2, the term number 
Term #3 is 8
Term #4 is 72 or 8×9 or 8×3², and 2 is half of 4, the term number
Term #5 is 9

So each odd term is the next term of 7,8,9,10,11,...
Then each even term is the preceding odd term times
3 raised to the power which is half the term number. 

So term #6 is 9×3³ since 3 is half the term number 6, 
and 9×3³ = 9×27 = 243.

Edwin