TechMathII - 1.2 - Sequences

Bell Ringer

Write in order from least to greatest.

1) -4/9, -2/5, -5/14

2) -6/14, -5/8, -21/45

3) 1/11, 2/19, 5/25

VocabularyVocabulary

SequencesSequences: numerical patterns in which : numerical patterns in which the numbers are arranged in a certain the numbers are arranged in a certain orderorder

TermsTerms: the numbers in a sequence: the numbers in a sequence

Continuing and Identifying a Continuing and Identifying a PatternPatternEx 1:

1.What is the perimeter (distance around) of the first figure:

2. What is the perimeter of the second figure?

3. What is the pattern in the perimeter of the figures?

4.What is the perimeter of the 6th and 10th figures?

Arithmetic SequencesArithmetic Sequences

- When the difference between two - When the difference between two consecutive terms of a sequence is the consecutive terms of a sequence is the samesame

““addingadding the same amount each time” the same amount each time”

- Common Difference- Common Difference

ExamplesExamplesFind the next three terms in each arithmetic Find the next three terms in each arithmetic sequence.sequence.

1) 25, 37, 49, 61, …1) 25, 37, 49, 61, …

2) 5, 11, 17, 23, …2) 5, 11, 17, 23, …

3) Z, ZYY, ZYXX, ZYXWW, …3) Z, ZYY, ZYXX, ZYXWW, …

4) A, AA, AAB, AABB, AABBC, …4) A, AA, AAB, AABB, AABBC, …

You try 1!You try 1!

Find the next three terms in each arithmetic Find the next three terms in each arithmetic sequence.sequence.

1) 1) -2, 5, 12, 19, …-2, 5, 12, 19, …

2)2) 135, 122, 109, …135, 122, 109, …

3) 3) 1/8, ¼, 3/8, ½, …1/8, ¼, 3/8, ½, …

4)4) -21, -32, -43, …-21, -32, -43, …

Geometric SequencesGeometric Sequences

- Each term is multiplied by a common - Each term is multiplied by a common number or factor to obtain the next termnumber or factor to obtain the next term

““multiplyingmultiplying by the same amount each by the same amount each time”time”

- Common Ratio- Common Ratio

ExamplesExamplesFind the next three terms in each geometric Find the next three terms in each geometric sequence.sequence.

1) 48, 24, 12, 6, …1) 48, 24, 12, 6, …

2) 3, 15, 75, 375, …2) 3, 15, 75, 375, …

3) 1, ½, ¼, …3) 1, ½, ¼, …

4) 352, -176, 88, -44, …4) 352, -176, 88, -44, …

You try 2!You try 2!

Find the next three terms in each geometric Find the next three terms in each geometric sequence.sequence.

1) 1) 1, -1, 1, -1, …1, -1, 1, -1, …

2)2) 135, 45, 15, …135, 45, 15, …

3) 3) 6, 30, 150, …6, 30, 150, …

4)4) 22500, 4500, 900, …22500, 4500, 900, …

You try 3! You try 3!

Decide whether each sequence is arithmetic or Decide whether each sequence is arithmetic or geometric. Then find the next three terms in each geometric. Then find the next three terms in each sequence.sequence.

1) 1) 1, 2, 4, 8, …1, 2, 4, 8, …

2)2) 13, 9, 5, …13, 9, 5, …

3) 3) 16, -4, 1, …16, -4, 1, …

4)4) -5, 0, 5, 10, …-5, 0, 5, 10, …

HomeworkHomework

Sequences WSSequences WS