What is the pattern rule for 1 2 4 8?

Answer 1

You are doubling the values each time. So it is U{n} = 2ⁿ⁻¹ for n = 1, 2, 3, 4.

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

Nothing can be said about values of U{n} beyond n = 4, as that above is only one of infinitely many functions which give the values {1, 2, 4, 8} for n = {1, 2, 3, 4}. For example:

In the above formula, U{5} = 16

But if U{n} = (27n⁴ - 266n³ + 933n² - 1318n + 648)/24

then U{1..4} are also {1, 2, 4, 8}, but U{5} = 42