Section 2.2 Geometric Sequences

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Presentation transcript:

Section 2.2 Geometric Sequences i) Terms, common ratio, number of terms in a geometric sequence ii) Geometric means iii) Solving Algebraic sequences © Copyright all rights reserved to Homework depot: www.BCMath.ca

I) What is a Geometric Sequence? A sequence where each term after the first is multiplied by a common ratio “r” Not the same as an arithmetic sequence (Add) © Copyright all rights reserved to Homework depot: www.BCMath.ca

II) Formula for Geometric Sequence: The value of the “nth” term Value of the 1st term Common Ratio - Divide any term by its previous term The rank of the term © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Given the following sequence, find the 20th term: Ex: given the three terms in a geometric sequence, find the common ratio: To find the common ratio, you can just take any term and divide it by the previous term So, the common ratio will be: © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Given and find the common ratio and the first term: Ex: the third term of a geometric sequence is 27 and the sixth term is 64. Find the common ratio: Each term in the sequence is equal to the previous term multiplied by the common ratio: The sixth term is equal to both 64 and 27r3 To find the terms in between, just multiply 27 by the common ratio. Ex: Given and find the common ratio and the first term: Now solve for the first term © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: If forms a geometric sequence. Solve for x. The new sequence formed is 1 , 2 , 4 which is a geometric sequence. Ex: The first and second terms of a geometric sequence have a sum of 15, while the second and third terms have a sum of 60. Use an algebraic method to find all three terms.

III) Terms & FINAL equation: Double Time: The time it takes a population or the weight of an object to double its size or value Half – Life: The time it takes a population or object to depreciate to half its size or value Ie: Time it takes a population to double Ie: Time required to reach Half - Life Annually: L = 1 © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Cockroach Question: If a colony of 2 cockroaches doubles every day, how many cockroaches will there be after 1 week? © Copyright all rights reserved to Homework depot: www.BCMath.ca

© Copyright all rights reserved to Homework depot: www.BCMath.ca

© Copyright all rights reserved to Homework depot: www.BCMath.ca

© Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: If a colony of 12 cockroaches doubles every 3 days, after how many days will the population be over 10,000? After 30 days, the population of the cockroaches will be over 10,000!! © Copyright all rights reserved to Homework depot: www.BCMath.ca

Let the first three terms be Ex: The first and second terms of a geometric sequence have a sum of 15, while the second and third terms have a sum of 60. Use an algebraic method to find all three terms. Let the first three terms be We will find r from the following system of two equations in two unknowns. Dividing equation (2) by equation (1) we can eliminate a.