How do you find out the nth term in quadratic sequences? - Answers

It's simpler than you might think.. The general equation you need is this: a+b+c 4a+2b+c 9a+3b+c 16a+4b+c 3a+b 5a+b 7a+b 2a 2a Basically, the second row down is the difference between the terms of the sequence itself (top row). And the 3rd row down is the differences of the differences (:P). I'm not good enough with words to explain how to find the nth term so I'll give you an example: 3 7 15 27 43 4 8 12 16 4 4 4 First, you need to know this formula: 2a=diff. of diff. (4 in this example) 3a+b= 1st of the differences (4 in this example) A+B+C= 1st term (3 in this example) So let's work it out: 2a=4 (so) a=2 3a+b= 4 (3a would be 3 times 2 so) 6+b=4 (To get from 6 to 4 you need to minus two so) b= -2 (To get to c you need a+b and then work out the difference of that and the 1st term.) a+b= 0 (2-2= 0) (The difference of the first term and a+b gives you c) 3-0= 3 c=3 Hope this has helped :S