Question

In this lesson, you compared a recursive rule and an explicit rule used to define a sequence. For example, in the sequence 1, 3, 6, 10, 15, 21, … a recursive rule is an = an-1 + n. An explicit rule for the same sequence is (n2 + n)/2. Which rule do you think is easier to use when finding a term in the sequence? Why?

Answer 1

I would imagine that it would be easier and much computationally more efficient to use the second formula to find a single term

Answer 2

using the recursive method you have to calculate all of the values before the one you are trying to find in order to get the answer

Answer 3

though in terms of computing power required I think that the recursive formula would be more efficient at low values of n

Answer 4

for a randomly chosen value of n, though, you would want to calculate using formula 2

Answer 5

ie: try doing the first formula for 1000

Answer 6

n = 1000

Answer 7

or you can do the second formula for 1000 in a few seconds

Answer 8

actually, if you try and make a program for a TI-84 calculator that uses the first algorithm, it runs out of memory when trying to compute n = 1000

Answer 9

if you make a program using algorithm 2, you can calculate n = 1000 in a split second

Answer 10

so 2 is definitely better for a single, random n