explicit form of sum of geometric sequence

#EXPLICIT FORM OF SUM OF GEOMETRIC SEQUENCE SERIES#

The general form of an arithmetic sequence can be written as: This difference can either be positive or negative, and dependent on the sign will result in terms of the arithmetic sequence tending towards positive or negative infinity. Arithmetic SequenceĪn arithmetic sequence is a number sequence in which the difference between each successive term remains constant. Indexing involves writing a general formula that allows the determination of the n th term of a sequence as a function of n.

In cases that have more complex patterns, indexing is usually the preferred notation. There are multiple ways to denote sequences, one of which involves simply listing the sequence in cases where the pattern of the sequence is easily discernible.

#EXPLICIT FORM OF SUM OF GEOMETRIC SEQUENCE SERIES#

They are particularly useful as a basis for series (essentially describe an operation of adding infinite quantities to a starting quantity), which are generally used in differential equations and the area of mathematics referred to as analysis. Sequences are used to study functions, spaces, and other mathematical structures. A series is convergent if the sequence converges to some limit, while a sequence that does not converge is divergent. Sequences have many applications in various mathematical disciplines due to their properties of convergence. There are many different types of number sequences, three of the most common of which include arithmetic sequences, geometric sequences, and Fibonacci sequences. In a number sequence, the order of the sequence is important, and depending on the sequence, it is possible for the same terms to appear multiple times. The individual elements in a sequence is often referred to as term, and the number of terms in a sequence is called its length, which can be infinite. Accordingly, a number sequence is an ordered list of numbers that follow a particular pattern. In mathematics, a sequence is an ordered list of objects. The resource at the bottom is a formula chart for geometric and arithmetic sequences and series.Example: 1, 3, 5, 7, 9 11, 13. The third resource is an arithmetic and geometric sequence and series game. The second resource would be a great follow up after teaching arithmetic sequences. I’m working on the geometric sequence activity now and hope to finish in a week or so. I’ve attached a couple more of my resources. I wanted to create something that students could learn from and see how these patterns are involved in real-life situations. When I was creating this resource, it really stretched my thinking. Some of the examples I used above are in my Arithmetic Sequence Activity seen below. Students need to know that their math is real and useful! I hope this encourages you to use some of these examples or make up some of your own. It’s really fun to create these problems. I hope I’ve given you plenty to think about. When you are finished reading this post, please consider filling out this feedback form called: Understanding Our Visitors. I’m happy for you to use these situations with your classes. Yes, but I want visuals! I also did not want the situation to be a direct variation or always positive numbers and always increasing or positive slopes.īelow are some of the situations I’ve come up with along with a picture. My recent thoughts have been about arithmetic sequences.

I’ve also tried to catch the situation in action, but it’s not always possible especially since sometimes I think of an idea while driving or when I’m falling asleep at night. I’ve made it a goal of mine to find real-life situations. When I was in college and the earlier part of my teaching career, I was all about the math… not how I might could use it in real life.

One of my goals as a math teacher is to present real-life math every chance I get.

Explicit form of sum of geometric sequence