Notes: Number Patterns – Arithmetic Sequences



Math 1: Sequences Name_____________________________________

5.1-1 Notes: Arithmetic Sequences

Sequence: another name for an ________________________________________.

Arithmetic Sequence: formed by ___________________ a fixed number to each previous term.

(ex) –4, 5, 14, 23

[pic] _______________

+_____ +_____ +_____ ___________________________________

*The best way to find the common difference is to subtract the _______________ term from the

________________________ term.

*NOTE: The common difference will be ___________________________ if the sequence is increasing and

_________________________ if the sequence is decreasing.

Example 1: Find the common difference of each arithmetic sequence.

(a) –7, –3, 1, 5, . . . (b) 8, 3, –2, –7, . . . (c) 5, 2, –1, –4, . . .

Example 2: Find the next two terms in each sequence.

(a) 20, 14, 8, 2, _____, _____ (b) 0.7, 1.5, 2.3, 3.1, _____, _____ (c) –5, 4, 13, 22, _____, _____

Example 3: Let n = the term number in the sequence and an = the value of the nth term of the sequence.

(a) Find the first, fifth, and tenth terms of the sequence that has the rule an = 12 + (n – 1)( –2).

(b) Find the first, sixth, and twelfth terms of the sequence that has the rule an = –5 + (n – 1)( 3).

(c) Find the first, fourth, and eleventh terms of the sequence that has the rule an = 7+ (n – 1)( 4).

Notes: Geometric Sequences

Geometric Sequence: formed by ___________________________ a fixed number to each previous term.

(ex) 2, 10, 50, 250

[pic]

×_____ ×_____ ×_____ ____________________________

*The best way to find the common ratio is to divide the _________________ term by the _____________ term and simplify.

Example 1: Find the common ratio of each geometric sequence.

(a) 3, 12, 48, 192, . . . (b) –3, –6, –12, –24, . . .

*NOTE: The common ratio is ___________________________ if all terms in the sequence are all positive OR all negative.

*NOTE: The common ratio can be a ___________________________!

(c) 750, 150, 30, 6, . . . (d) –88, –44, –22, –11, . . .

*NOTE: The common ratio is ___________________________ if the signs of the terms in a sequence alternate between positive and negative.

(e) 2, –6, 18, –54, . . . (f) 3, –15, 75, –375, . . .

Example 2: Find the next three terms in each sequence.

(a) 1, 3, 9, 27, _____, _____, _____ (b) 120, –60, 30, –15, _____, _____, _____

Example 3: Let n = the term number in the sequence and an = the value of the nth term of the sequence.

(a) Find the first, fifth, and tenth terms of the sequence that has the rule [pic].

(b) Find the first, sixth, and twelfth terms of the sequence that has the rule [pic].

(c) Find the first, fourth, and eleventh terms of the sequence that has the rule [pic].

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