University:
College
Course:
College Mathematics
Academic year:

2023
Views:

24

Pages:

2
Author:

anon

Mathematics: Introduction to Sequences What is an Arithmetic Sequence? I think to start off, we should first briefly describe an Arithmetic Sequence. An arithmetic sequence is basically an ordered sequence of objects. Basically, there’s already a defined pattern in the sequence. If you don’t understand what I’m talking about, take a look at the examples below: 1. 1,2,3,4,5.. 2. 3,5,7,9,11.. 3. M,T,W,T.. 4. J,F,M,A… So, basically, you are trying to find out whats next. And we know that there is a structured pattern to this sequence. So lets try to analyze the five examples above. 1. I don’t think there needs any analysis for this one. Each term is simply being added by 1, so the next term will be 6. 2. What do you notice here? Yes, each term is being added by 2, and this is done on each term, so the next term will logically be added by 2 as well, so the answer will be 13. 3. Just because its maths, it doesn’t mean that all sequences need to be expressed in numbers. Its perfectly fine to have letters, words, symbols, shapes, photos, etc, as long as there is some structured pattern. This sequence is simply the first letter of each day of the week (Monday, Tuesday, Wednesday, Thursday), so the next term is obviously Friday, F. 4. Again, this is simply the months of the year, so the next term will obviously be May, M. Before we continue, we need to define some mathematical notations, which is basically a way to define certain concepts. The ones you will need to memorize for this topic are: Un:This i known as the nth term of the sequence, so U1 is the first term of the seqeuence, U2 the second. Sn:This is the sum of the first n terms. For example, if you have the seqeuence 6,10,14. How many terms doesit have? 3. So Sn will be the sum of the three terms 6+10+14=30 Next topic will introduce the concept of Arithmetic Sequences.