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"Describing Sequences" Review Assignment

What is a sequence?

Can you find the next term in the following sequence: $1, 5, 2, 10, 3, 15, \dots$

What is a closed formula for a sequence?

What does a recursive definition for a sequence consist of?

Write out the first 5 terms (starting with $a_{0}$ ) of the sequence described below. Then give either a closed formula or a recursive definition for the sequence (whichever is NOT given in the problem).

$a_{n} = n a_{n - 1}$ with $a_{0} = 1$

What is a partial sum?

Expand the following product. That is, write it out the long way. (List the first five terms before giving a final answer).
$\prod_{k = 0}^{n}_{} 2 + 3 k$

Find the closed formula for the following sequence by relating it to a well known sequence.
$2, 5, 10, 17, 26, \dots$

What is a sequence?

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Instructor solution

Christopher KennyNOV 25, 2021, 8:09:08 AM

A sequence is simply an ordered list of numbers.

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Discrete Mathematics: An Open Introduction (pages 152, 153)

Levin, O. (2018-12-31). Discrete Mathematics: An Open Introduction. . (Nov 25, 2021)

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True or False: The set $N$ is a sequence.

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True

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