Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a...
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Transcript of Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a...
![Page 1: Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.](https://reader035.fdocuments.in/reader035/viewer/2022081908/56649ef65503460f94c0a056/html5/thumbnails/1.jpg)
Arithmetic Sequences
Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.
![Page 2: Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.](https://reader035.fdocuments.in/reader035/viewer/2022081908/56649ef65503460f94c0a056/html5/thumbnails/2.jpg)
Arithmetic Sequences
Sequence: a list of numbers in a specific order.
Term: each number in a sequence
![Page 3: Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.](https://reader035.fdocuments.in/reader035/viewer/2022081908/56649ef65503460f94c0a056/html5/thumbnails/3.jpg)
Arithmetic Sequences
Arithmetic Sequence: a sequence in which each term after the first term is found by adding a constant, called the common difference (d), to the previous term.
Common Difference : refers to the difference between a given term and the next term in an arithmetic sequence.
![Page 4: Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.](https://reader035.fdocuments.in/reader035/viewer/2022081908/56649ef65503460f94c0a056/html5/thumbnails/4.jpg)
Find the Common Difference
82, 76, 70, 64
What is the common difference of the arithmetic sequence?
Find the next 3 terms in the sequence.
82, 76, 70, 64,
-6
58, 52, 46
![Page 5: Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.](https://reader035.fdocuments.in/reader035/viewer/2022081908/56649ef65503460f94c0a056/html5/thumbnails/5.jpg)
Recursive Form
Use the recursive form to find the next term or the next few terms in an arithmetic sequence.
tn = tn-1 + d
d = the common difference
n = the term you are wanting to find
Find the next term of the following arithmetic sequence using the formula above.
3, 6, 9, 12
![Page 6: Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.](https://reader035.fdocuments.in/reader035/viewer/2022081908/56649ef65503460f94c0a056/html5/thumbnails/6.jpg)
Closed Form
Use the closed formula to find the nth term of an arithmetic sequence.
an = a1 + (n – 1)dn = the term you are wanting to find
a1= the first term of the sequenced = the common differenceFind the 201st term of the following sequence using
the formula above:82, 76, 70, 64
a201 = 82 + (201 – 1)(-6)
a201 = -1118