Nth Terms of Other Sequences

## Nth Terms of Other Sequences

Sequences can be built on formulae. The formulae are based on two main elements: n, which is the current term, and U_n, which is the value of the term n.

U_(n-1) is the value of the term immediately prior to the nth term. This terminology allows for more complex sequences to be created.

this allows some complex manipulation of terms. For example, U_(n-1)^2 xx n means take the value of the previous term and square it, then multiply that by the current term.

## Example 1

What are the first five terms of the sequence given by U_n = n^2 - n?

 Term 1 2 3 4 5 n2 1 4 9 16 25 n 1 2 3 4 5 U_n = n2-n 0 2 6 12 20

Answer: 0, 2, 6, 12, 20

## Example 2

Write, in terms of U and n, a sequence where the value of the term is equal to the values of the previous two terms.

The value of the current term is given by U_n, the previous values are given by U_(n-1) (the value of the term before) and U_(n-2) (the value of the term before that).

This is the Fibonacci sequence.

Answer: U_n =U_(n-1) + U_(n-2)