Concept explainers
The difference between a sequence and series. Include in your discussion how to distinguish arithmetic, geometric, and Fibonacci-type sequence, and give the formulas for their general terms.
Explanation of Solution
The distinguishing a series from a sequence,
A sequences represent the list of numbers having a first term, a second term and so on and it is denoted as
Arithmetic: A sequence with a common difference,
Fibonacci: A sequence with first two term given, and subsequence terms the sum of the two previous terms. and its denoted as
A series represent sum of term of a sequence
Arithmetic series: Sum of the term of an arithmetic sequence:
Geometric series: Sum of the term of an geometric sequence:
Fibonacci series:
A sequence with first two terms given, and subsequence terms the sum of the two previous terms.
Want to see more full solutions like this?
Chapter 11 Solutions
Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term
- Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series 2.5,4,5.5,arrow_forwardFind a formula for the nth term of the geometric sequence 4, 20, 100, . . . .What is the 12th term of the sequence?arrow_forwardThe 5th term of an arithmetic sequence is 45, and the 12th term is 24. Find the nth term.arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill