M114

Sequence And Series

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Sequences and Series

Definition:

A sequence is an ordered list of numbers and the sum of the terms of a sequence is a series. In an arithmetic sequence, each term is equal to the previous term, plus (or minus) a constant. The constant is called the common difference (d).

HOW TO:

The formula for finding any term of an arithmetic sequence is where (a) is the first term of the sequence, d is the common difference, and n is the number of the term to find. To find the sum of a certain number of terms of an arithmetic sequence use where Snis the sum of n terms, (a) is the first term, and (a)n is the nth term. An arithmetic sequence graphs as points along a line.

Khan Link:

https://www.khanacademy.org/math/algebra2/sequences-and-series/alg2-geometric-sequence-series/v/series-as-sum-of-sequence

https://www.khanacademy.org/math/algebra/sequences/introduction-to-arithmetic-squences/v/arithmetic-sequences

https://www.khanacademy.org/math/algebra2/sequences-and-series/alg2-seq-and-series/v/formula-for-arithmetic-series

Lyrics

Sequence and Series

Sequences and series

A sequence is a set of things that are in order

Sequences and series

A series is a sum of those things that are in order

A sequence is an ordered listed things like numbers

That share some logical relationship such as 1,4,9,16,25

Which are the squared products of 1, 2,3,4,5

The list of numbers from 1 to 25 are called primes

And in formulas unknown terms are defined by variables

Like a with a little bity n at the foot of it

That’s an index it shows the order of the term it numbers it

Like a with an index 1 and a with an index 2

Is a sub 1 and a sub 2

That denotes the first two terms of the sequence

And finding the terms and adding them up is the reason for

Sequences and series

A sequence is a set of things that are in order

Sequences and series

A series is a sum of those things that are in order

Standards

CCSS.MATH.CONTENT.7.SP.C.7.A — Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
CCSS.MATH.CONTENT.7.SP.C.7 — Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
CCSS.MATH.CONTENT.7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.