Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a...

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Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.

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.

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.

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.

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.

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.

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.

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