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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)`