Concept explainers
A new start. Suppose we build a sequence of numbers using the method of adding the previous two numbers to build the next one. This time, however, suppose our first two numbers are 2 and 1. Generate the first 15 terms. This sequence is called the Lucas sequence and is written as L1, L2, L3, …. Compute the quotients of consecutive terms of the Lucas sequence as we did with the Fibonacci numbers. What number do these quotients approach? What role do the initial values play in determining what number the quotients approach? Try two other first terms and generate a sequence. What do the quotients approach?
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Additional Math Textbook Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
A Survey of Mathematics with Applications (10th Edition) - Standalone book
- Determine if each sequence is arithmetic. If so, indicate the common difference. (a) 9,20,31,42,53,64,... (b) 12,6,0,6,12,18,... (c) 7,1,10,4,13,7,...arrow_forwardWrite an explicit formula for the arithmetic sequence 15.6,15,14.4,13.8,... and then find the 32 term.arrow_forwardFind the next term of each sequence a,ar,ar2,ar3,....arrow_forward
- Find the first term and common difference of a sequence where the third term is 2 and the twelfth term is -25. Give the formula for the general term.arrow_forwardThe 5th term of an arithmetic sequence is 45, and the 12th term is 24. Find the nth term.arrow_forwardFind the 5thterm of the arithmetic sequence 9b,5b,b, .arrow_forward
- Find the ninth term of the sequence 6,18,54,162,486,1,458,... Then find the general term for the sequence.arrow_forwardThe 8th term of an arithmetic sequence is 25, and the 12th term is 41. Write the first 11 terms of this sequence.arrow_forwardFind the eleventh term of the sequence 7,14,28,112,224,... Then find the general term for the sequence.arrow_forward
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill