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 *n*^{th} 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*.

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

Term | 1 | 2 | 3 | 4 | 5 |

n^{2} |
1 | 4 | 9 | 16 | 25 |

n |
1 | 2 | 3 | 4 | 5 |

`U_n` = n^{2}-n |
0 | 2 | 6 | 12 | 20 |

Answer: 0, 2, 6, 12, 20

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)`

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