Find the nth term for the following:
1) 12, 30, 56, 90, 132
What you arre looking for is a pattern. Some rule or procedure that generates the terms and tells you how to find the next term. Sometimes the pattern is clear and sometimes you have to play with the numbers to discover the pattern. Here is one method that works for your first problem.
Looking at the terms themselves I don't see any pattern. First I am going to find the difference between each term and the next term. The difference between the first two terms is 18. The difference between the second and third terms is 26, etc. I want to keep track in a table. The first row is the sequence and the second row is the differences.
This row definitely has a pattern! They are all 8. If this pattern repeats then the next term in the third row is also 8 so the next term in the second row must be 50. (It has to be 50 because 50 - 42 = 8.) This in turn gives the next term in the first row as 82.