![]() ![]() Let's analyze a simple example that can be solved using the arithmetic sequence formula. This formula will allow you to find the sum of an arithmetic sequence. Substituting the arithmetic sequence equation for nᵗʰ term: All you have to do is to add the first and last term of the sequence and multiply that sum by the number of pairs (i.e., by n/2). That means that we don't have to add all numbers. ![]() The sum of each pair is constant and equal to 24. We will add the first and last term together, then the second and second-to-last, third and third-to-last, etc. Let's try to sum the terms in a more organized fashion. We could sum all of the terms by hand, but it is not necessary. Look at the first example of an arithmetic sequence: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Trust us, you can do it by yourself - it's not that hard! Our arithmetic sequence calculator can also find the sum of the sequence (called the arithmetic series) for you. A perfect spiral - just like this one! (Credit: Wikimedia.) If you drew squares with sides of length equal to the consecutive terms of this sequence, you'd obtain a perfect spiral. ![]() It's worth your time.Ī great application of the Fibonacci sequence is constructing a spiral. ![]() Interesting, isn't it? So if you want to know more, check out the fibonacci calculator. Each term is found by adding up the two terms before it. This is not an example of an arithmetic sequence, but a special case called the Fibonacci sequence. Now, let's take a close look at this sequence:Ĭan you deduce what is the common difference in this case? What happens in the case of zero difference? Well, you will obtain a monotone sequence, where each term is equal to the previous one. Naturally, if the difference is negative, the sequence will be decreasing. If the common difference of an arithmetic sequence is positive, we call it an increasing sequence. In fact, it doesn't even have to be positive! JS Graphics JS Graphics JS Canvas JS Plotly JS Chart.js JS Google Chart JS D3.Some examples of an arithmetic sequence include:Ĭan you find the common difference of each of these sequences? Hint: try subtracting a term from the following term.īased on these examples of arithmetic sequences, you can observe that the common difference doesn't need to be a natural number - it could be a fraction. JS vs jQuery jQuery Selectors jQuery HTML jQuery CSS jQuery DOM JS JSON JSON Intro JSON Syntax JSON vs XML JSON Data Types JSON Parse JSON Stringify JSON Objects JSON Arrays JSON Server JSON PHP JSON HTML JSON JSONP JS AJAX AJAX Intro AJAX XMLHttp AJAX Request AJAX Response AJAX XML File AJAX PHP AJAX ASP AJAX Database AJAX Applications AJAX Examples JS Web APIs Web API Intro Web Forms API Web History API Web Storage API Web Worker API Web Fetch API Web Geolocation API JS Browser BOM JS Window JS Screen JS Location JS History JS Navigator JS Popup Alert JS Timing JS Cookies JS HTML DOM DOM Intro DOM Methods DOM Document DOM Elements DOM HTML DOM Forms DOM CSS DOM Animations DOM Events DOM Event Listener DOM Navigation DOM Nodes DOM Collections DOM Node Lists JS Async JS Callbacks JS Asynchronous JS Promises JS Async/Await JS Classes Class Intro Class Inheritance Class Static JS Functions Function Definitions Function Parameters Function Invocation Function Call Function Apply Function Bind Function Closures JS Objects Object Definitions Object Properties Object Methods Object Display Object Accessors Object Constructors Object Prototypes Object Iterables Object Sets Object Maps Object Reference JS Tutorial JS HOME JS Introduction JS Where To JS Output JS Statements JS Syntax JS Comments JS Variables JS Let JS Const JS Operators JS Arithmetic JS Assignment JS Data Types JS Functions JS Objects JS Events JS Strings JS String Methods JS String Search JS String Templates JS Numbers JS BigInt JS Number Methods JS Number Properties JS Arrays JS Array Methods JS Array Sort JS Array Iteration JS Array Const JS Dates JS Date Formats JS Date Get Methods JS Date Set Methods JS Math JS Random JS Booleans JS Comparisons JS If Else JS Switch JS Loop For JS Loop For In JS Loop For Of JS Loop While JS Break JS Iterables JS Sets JS Maps JS Typeof JS Type Conversion JS Bitwise JS RegExp JS Precedence JS Errors JS Scope JS Hoisting JS Strict Mode JS this Keyword JS Arrow Function JS Classes JS Modules JS JSON JS Debugging JS Style Guide JS Best Practices JS Mistakes JS Performance JS Reserved Words ![]()
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