What is the next number in the sequence?
1, 4, 13, 40,

The pattern here is the number times 3 then plus 1

We can check this by plugging it in.

1×3=3
3+1=4
4 is the next number in our sequence so the pattern works.

We can continue to check this with the rest of our sequence.

4×3=12
12+1=13
13 is the next number in our sequence so the pattern works.

13×3=39
39+1=40
40 is the next number in our sequence so the pattern works.

40×3=120
120+1=121
121 is the next number in our sequence so the pattern works.

We can find the next numbed in the sequence by continuing the patter
121×3=363
363+1=364

So the next number in the sequence is 364