How can you represent the terms of a sequence explicitly? How can you represent them recursively? Provide mathematical examples to support your opinions.

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Mathematics

Ansley Tran

17 August, 03:30

How can you represent the terms of a sequence explicitly? How can you represent them recursively? Provide mathematical examples to support your opinions.

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Karlie Pace · Answer 1

1/Explicitly: with a formula that contains and uses n, the term number.

Example. The sequence 9, 12, 15, 18 ... can be represented by the formula an = 3n + 6.

2/Recursively: with a formula containing and using a (n-1), the previous term.

Example: 9, 12, 15, 18 ... can be represented by the formula an = a (n-1) + 3. The first term (a1) needs to be specified (a1 = 9)