Algebra 1 Arithmetic and Geometric Sequences April 21, 2020

We will continue working on sequences today:
Here are some notes. Your classwork
Arithmetic Sequences
Example:

1, 4, 7, 10, 13, 16, 19, 22, 25, ...

Its Rule is x_n = 3n-2

• a is the first term, and

• d is the difference between the terms (called the "common difference")

Geometric Sequences
Example:

2, 4, 8, 16, 32, 64, 128, 256, ...

Its Rule is x_n = 2ⁿ

• a is the first term, and

• r is the factor between the terms (called the "common ratio")

• When r=0, we get the sequence {a,0,0,...} which is not geometric

is posted after the notes. See you at the zoom call at 1 p.m.

In an Arithmetic Sequence the difference between one term and the next is a constant.
In other words, we just add some value each time ... on to infinity.
This sequence has a difference of 3 between each number.
In General we can write an arithmetic sequence like this:
{a, a+d, a+2d, a+3d, ... }
where:
And we can make the rule:
x_n = a + d(n-1)(We use "n-1" because d is not used in the 1st term).

In a Geometric Sequence each term is found by multipl

ying the previous term by a constant.
This sequence has a factor of 2 between each number.
In General we can write a geometric sequence like this:
{a, ar, ar², ar³, ... }
where:
Note: r should not be 0.
And the rule is:
x_n = ar^(n-1)(We use "n-1" because ar⁰ is the 1st term)
source:
https://www.mathsisfun.com/algebra/sequences-series.html

Assignment:

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