For number patterns, my teacher gave me a method to find the equations...
First, find the diffrence between all the 2 consecutive numbers.
(1) If the differences are the same in the very first try, the equation to find the n
th term will be in the first degree, which is:
nth Term = an + b,
Now replace a & b with numbers. You gotta do this by trial and error, I think.
(2) If the differnces are different in the first try, find the differences of the preveious differences. If they are same here, in the second try, the equation to find the n
th term will be in the second degree, which is:
nth Term = an2 + bn + c
Now replace a, b & c with numbers. You gotta do this by trial and error, I think.
(3) If the diffrences are still diffrenet in the second try, ind the differences of the preveious differences. If they are the same, in the third try, the equation to find the n
th term will be in the third degree, which is:
nth Term = an3 + bn2 + cn + d
Now replace a, b, c, & d with numbers. You gotta do this by trial and error, I think.
It's kind of long when you do it the first time, but once you get used to, it's easy, yet long. But it'll always get you the correct numbers. Most often, you just guess some of the equations. Like try- n
2, n
3, (n+/-1)
2, and such.
You need lots of practice to do these quickly in the exams. Hopefully, I've practiced enough.
Hope I helped. All the best, guys.