How do you write a formula for number patterns?

Answer 1

As a first step, you need to experiment a bit, until you find manage to figure out the rule underlying the pattern. After that, you may need further experimentation until you find the correct formula. Here are some special cases.* If the difference between two consecutive numbers is constant, you use an algebraic sequence. Example: each number is 3 more than the previous one. The sequence is of the type 3n + (some constant). You can find out the constant quite quickly, by experimenting a bit.

* If the difference increases by a constant amount, for example the differences are 1, 2, 3, 4, 5, ..., some quadratic formula should work.

* If the RATIO between two consecutive numbers is a constant, it's a geometric sequence, of the form a times b to the power n. "b" is the ratio; once again, you can figure out "a" by experimenting.

Answer 2

There are different ways to find and express formulae for number patterns: some are position to value, some are iterative.