Sequences Flashcards
How do you find the position-to-term rule for a quadratic sequence?
First you find the differences between the numbers in the sequence (in a quadratic sequence they should all be different) (e.g 3, 9, 19, 33, 51 and the differences are 6, 10, 14, 18) then you find the difference between the differences (in a quadratic sequence they should all be the same) (in this case the difference of the differences is 4). You then divide the second difference by 2 (which equals 2 in this example) then put that in front of nsquared (2nsquared in this case). To find the rest of the formula you put 1 into the formula you’ve found so far (so T(1) = 2nsquared = 2 (because 1 x 1 = 1 and 1 x 2 = 2) and take your answer from the first number in the original sequence (so 3 - 2 = 1 or +1) and put that at the end of the formula (so the final formula is 2nsquared+1). You can also do this in a table.
How do you find the posititon-to-term rule (formula) for a linear sequence?
First you find the difference between the numbers in the sequence (in a linear sequence, all of the differences should be the same) so for example in 4, 7, 10, 13, 16, 19 the differences are all 3. This means that the formula begins with 3n. To find the rest, you must take the difference (3) from the first number in the sequence (which in the case is 4, so 4 - 3 = 1 which is the same as +1), you put the result at the end of the formula (so the formula is 3n+1).
